Algebra for algebraic topology












2














My research is in analysis, but it moved to the area that requires algebraic topology. I have some working knowledge in that area, but I always feel that I am on a shaky ground and I need to go back and study algebraic topology again. However, that would also require refreshing my knowledge in algebra. My question is:




What is a good reference from which I could learn algebra necessary
for studying algebraic topology at the level of Hatcher's Algebraic Topology plus Eilenberg-Steenrod's axioms (not included in Hatcher's book) plus spectral sequences (in unpublished notes of Hatcher).




I would love to find an elementary reference that would cover all necessary algebraic tools (including homological algebra) on no more than 100$pmvarepsilon$ pages.






at.algebraic-topology ac.commutative-algebra homological-algebra







share|cite|improve this question




















  • 1




    That depends very much on what parts of algebraic topology you want to use and for what purpose. Further details would be helpful.
    – Neil Strickland
    6 hours ago










  • @NeilStrickland I added more details to my question.
    – Piotr Hajlasz
    6 hours ago










  • Serge Lang's Algebra covers what you need, but it's more than 100 pages. Dummit and Foot is a nice undergraduate algebra book that covers essentially all you need, although it does not really develop homological algebra -- but you don't really need to know any homological algebra to study from Hatcher's book. Dummit and Foot is also over 100 pages. I imagine there is something that satisfies all your criteria. The undergraduate books all are a little longwinded compared to what you are looking for.
    – Ryan Budney
    6 hours ago






  • 3




    @RyanBudney Dummit and Foote: 932 pages, Lang: 914 pages. That is precisely what I would like to avoid. I actually do not like the book by Dummit and Foote: a lot of unnecessary words, like in most of the undergraduate texts.
    – Piotr Hajlasz
    6 hours ago








  • 2




    amazon.com/Algebra-Chapter-Graduate-Studies-Mathematics/dp/… is again long, but covers much more ground than Dummit & Foote (and you can safely skip the irrelevant to you chapters, it's much nicer structured than D and F IMHO)
    – Dima Pasechnik
    47 mins ago
















2














My research is in analysis, but it moved to the area that requires algebraic topology. I have some working knowledge in that area, but I always feel that I am on a shaky ground and I need to go back and study algebraic topology again. However, that would also require refreshing my knowledge in algebra. My question is:




What is a good reference from which I could learn algebra necessary
for studying algebraic topology at the level of Hatcher's Algebraic Topology plus Eilenberg-Steenrod's axioms (not included in Hatcher's book) plus spectral sequences (in unpublished notes of Hatcher).




I would love to find an elementary reference that would cover all necessary algebraic tools (including homological algebra) on no more than 100$pmvarepsilon$ pages.






at.algebraic-topology ac.commutative-algebra homological-algebra







share|cite|improve this question




















  • 1




    That depends very much on what parts of algebraic topology you want to use and for what purpose. Further details would be helpful.
    – Neil Strickland
    6 hours ago










  • @NeilStrickland I added more details to my question.
    – Piotr Hajlasz
    6 hours ago










  • Serge Lang's Algebra covers what you need, but it's more than 100 pages. Dummit and Foot is a nice undergraduate algebra book that covers essentially all you need, although it does not really develop homological algebra -- but you don't really need to know any homological algebra to study from Hatcher's book. Dummit and Foot is also over 100 pages. I imagine there is something that satisfies all your criteria. The undergraduate books all are a little longwinded compared to what you are looking for.
    – Ryan Budney
    6 hours ago






  • 3




    @RyanBudney Dummit and Foote: 932 pages, Lang: 914 pages. That is precisely what I would like to avoid. I actually do not like the book by Dummit and Foote: a lot of unnecessary words, like in most of the undergraduate texts.
    – Piotr Hajlasz
    6 hours ago








  • 2




    amazon.com/Algebra-Chapter-Graduate-Studies-Mathematics/dp/… is again long, but covers much more ground than Dummit & Foote (and you can safely skip the irrelevant to you chapters, it's much nicer structured than D and F IMHO)
    – Dima Pasechnik
    47 mins ago














2












2








2







My research is in analysis, but it moved to the area that requires algebraic topology. I have some working knowledge in that area, but I always feel that I am on a shaky ground and I need to go back and study algebraic topology again. However, that would also require refreshing my knowledge in algebra. My question is:




What is a good reference from which I could learn algebra necessary
for studying algebraic topology at the level of Hatcher's Algebraic Topology plus Eilenberg-Steenrod's axioms (not included in Hatcher's book) plus spectral sequences (in unpublished notes of Hatcher).




I would love to find an elementary reference that would cover all necessary algebraic tools (including homological algebra) on no more than 100$pmvarepsilon$ pages.






at.algebraic-topology ac.commutative-algebra homological-algebra







share|cite|improve this question















My research is in analysis, but it moved to the area that requires algebraic topology. I have some working knowledge in that area, but I always feel that I am on a shaky ground and I need to go back and study algebraic topology again. However, that would also require refreshing my knowledge in algebra. My question is:




What is a good reference from which I could learn algebra necessary
for studying algebraic topology at the level of Hatcher's Algebraic Topology plus Eilenberg-Steenrod's axioms (not included in Hatcher's book) plus spectral sequences (in unpublished notes of Hatcher).




I would love to find an elementary reference that would cover all necessary algebraic tools (including homological algebra) on no more than 100$pmvarepsilon$ pages.






at.algebraic-topology ac.commutative-algebra homological-algebra




at.algebraic-topology ac.commutative-algebra homological-algebra






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited 6 hours ago

























asked 7 hours ago









Piotr Hajlasz

6,02142253




6,02142253








  • 1




    That depends very much on what parts of algebraic topology you want to use and for what purpose. Further details would be helpful.
    – Neil Strickland
    6 hours ago










  • @NeilStrickland I added more details to my question.
    – Piotr Hajlasz
    6 hours ago










  • Serge Lang's Algebra covers what you need, but it's more than 100 pages. Dummit and Foot is a nice undergraduate algebra book that covers essentially all you need, although it does not really develop homological algebra -- but you don't really need to know any homological algebra to study from Hatcher's book. Dummit and Foot is also over 100 pages. I imagine there is something that satisfies all your criteria. The undergraduate books all are a little longwinded compared to what you are looking for.
    – Ryan Budney
    6 hours ago






  • 3




    @RyanBudney Dummit and Foote: 932 pages, Lang: 914 pages. That is precisely what I would like to avoid. I actually do not like the book by Dummit and Foote: a lot of unnecessary words, like in most of the undergraduate texts.
    – Piotr Hajlasz
    6 hours ago








  • 2




    amazon.com/Algebra-Chapter-Graduate-Studies-Mathematics/dp/… is again long, but covers much more ground than Dummit & Foote (and you can safely skip the irrelevant to you chapters, it's much nicer structured than D and F IMHO)
    – Dima Pasechnik
    47 mins ago














  • 1




    That depends very much on what parts of algebraic topology you want to use and for what purpose. Further details would be helpful.
    – Neil Strickland
    6 hours ago










  • @NeilStrickland I added more details to my question.
    – Piotr Hajlasz
    6 hours ago










  • Serge Lang's Algebra covers what you need, but it's more than 100 pages. Dummit and Foot is a nice undergraduate algebra book that covers essentially all you need, although it does not really develop homological algebra -- but you don't really need to know any homological algebra to study from Hatcher's book. Dummit and Foot is also over 100 pages. I imagine there is something that satisfies all your criteria. The undergraduate books all are a little longwinded compared to what you are looking for.
    – Ryan Budney
    6 hours ago






  • 3




    @RyanBudney Dummit and Foote: 932 pages, Lang: 914 pages. That is precisely what I would like to avoid. I actually do not like the book by Dummit and Foote: a lot of unnecessary words, like in most of the undergraduate texts.
    – Piotr Hajlasz
    6 hours ago








  • 2




    amazon.com/Algebra-Chapter-Graduate-Studies-Mathematics/dp/… is again long, but covers much more ground than Dummit & Foote (and you can safely skip the irrelevant to you chapters, it's much nicer structured than D and F IMHO)
    – Dima Pasechnik
    47 mins ago








1




1




That depends very much on what parts of algebraic topology you want to use and for what purpose. Further details would be helpful.
– Neil Strickland
6 hours ago




That depends very much on what parts of algebraic topology you want to use and for what purpose. Further details would be helpful.
– Neil Strickland
6 hours ago












@NeilStrickland I added more details to my question.
– Piotr Hajlasz
6 hours ago




@NeilStrickland I added more details to my question.
– Piotr Hajlasz
6 hours ago












Serge Lang's Algebra covers what you need, but it's more than 100 pages. Dummit and Foot is a nice undergraduate algebra book that covers essentially all you need, although it does not really develop homological algebra -- but you don't really need to know any homological algebra to study from Hatcher's book. Dummit and Foot is also over 100 pages. I imagine there is something that satisfies all your criteria. The undergraduate books all are a little longwinded compared to what you are looking for.
– Ryan Budney
6 hours ago




Serge Lang's Algebra covers what you need, but it's more than 100 pages. Dummit and Foot is a nice undergraduate algebra book that covers essentially all you need, although it does not really develop homological algebra -- but you don't really need to know any homological algebra to study from Hatcher's book. Dummit and Foot is also over 100 pages. I imagine there is something that satisfies all your criteria. The undergraduate books all are a little longwinded compared to what you are looking for.
– Ryan Budney
6 hours ago




3




3




@RyanBudney Dummit and Foote: 932 pages, Lang: 914 pages. That is precisely what I would like to avoid. I actually do not like the book by Dummit and Foote: a lot of unnecessary words, like in most of the undergraduate texts.
– Piotr Hajlasz
6 hours ago






@RyanBudney Dummit and Foote: 932 pages, Lang: 914 pages. That is precisely what I would like to avoid. I actually do not like the book by Dummit and Foote: a lot of unnecessary words, like in most of the undergraduate texts.
– Piotr Hajlasz
6 hours ago






2




2




amazon.com/Algebra-Chapter-Graduate-Studies-Mathematics/dp/… is again long, but covers much more ground than Dummit & Foote (and you can safely skip the irrelevant to you chapters, it's much nicer structured than D and F IMHO)
– Dima Pasechnik
47 mins ago




amazon.com/Algebra-Chapter-Graduate-Studies-Mathematics/dp/… is again long, but covers much more ground than Dummit & Foote (and you can safely skip the irrelevant to you chapters, it's much nicer structured than D and F IMHO)
– Dima Pasechnik
47 mins ago










1 Answer
1






active

oldest

votes


















3














If you need a concise but very clear book which covers a lot of Algebraic Topology and just the necessary algebra (spectral sequences as well) I think that Differential Forms in Algebraic Topology- Bott & Tu is the book you are looking for.






share|cite|improve this answer





















  • I know this book, but it does not really provides a good introduction to algebra. Moreover, the deRham approach to topology gives only real coefficients and neglects the torsion part.
    – Piotr Hajlasz
    5 hours ago






  • 3




    Ah! Probably I found the right textbook! Try to take a look at Topology and geometry-Bredon :) It covers the necessary algebra along the way and begins with the basic topics of Algebraic Topology.
    – Vincenzo Zaccaro
    5 hours ago













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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









3














If you need a concise but very clear book which covers a lot of Algebraic Topology and just the necessary algebra (spectral sequences as well) I think that Differential Forms in Algebraic Topology- Bott & Tu is the book you are looking for.






share|cite|improve this answer





















  • I know this book, but it does not really provides a good introduction to algebra. Moreover, the deRham approach to topology gives only real coefficients and neglects the torsion part.
    – Piotr Hajlasz
    5 hours ago






  • 3




    Ah! Probably I found the right textbook! Try to take a look at Topology and geometry-Bredon :) It covers the necessary algebra along the way and begins with the basic topics of Algebraic Topology.
    – Vincenzo Zaccaro
    5 hours ago


















3














If you need a concise but very clear book which covers a lot of Algebraic Topology and just the necessary algebra (spectral sequences as well) I think that Differential Forms in Algebraic Topology- Bott & Tu is the book you are looking for.






share|cite|improve this answer





















  • I know this book, but it does not really provides a good introduction to algebra. Moreover, the deRham approach to topology gives only real coefficients and neglects the torsion part.
    – Piotr Hajlasz
    5 hours ago






  • 3




    Ah! Probably I found the right textbook! Try to take a look at Topology and geometry-Bredon :) It covers the necessary algebra along the way and begins with the basic topics of Algebraic Topology.
    – Vincenzo Zaccaro
    5 hours ago
















3












3








3






If you need a concise but very clear book which covers a lot of Algebraic Topology and just the necessary algebra (spectral sequences as well) I think that Differential Forms in Algebraic Topology- Bott & Tu is the book you are looking for.






share|cite|improve this answer












If you need a concise but very clear book which covers a lot of Algebraic Topology and just the necessary algebra (spectral sequences as well) I think that Differential Forms in Algebraic Topology- Bott & Tu is the book you are looking for.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered 5 hours ago









Vincenzo Zaccaro

346312




346312












  • I know this book, but it does not really provides a good introduction to algebra. Moreover, the deRham approach to topology gives only real coefficients and neglects the torsion part.
    – Piotr Hajlasz
    5 hours ago






  • 3




    Ah! Probably I found the right textbook! Try to take a look at Topology and geometry-Bredon :) It covers the necessary algebra along the way and begins with the basic topics of Algebraic Topology.
    – Vincenzo Zaccaro
    5 hours ago




















  • I know this book, but it does not really provides a good introduction to algebra. Moreover, the deRham approach to topology gives only real coefficients and neglects the torsion part.
    – Piotr Hajlasz
    5 hours ago






  • 3




    Ah! Probably I found the right textbook! Try to take a look at Topology and geometry-Bredon :) It covers the necessary algebra along the way and begins with the basic topics of Algebraic Topology.
    – Vincenzo Zaccaro
    5 hours ago


















I know this book, but it does not really provides a good introduction to algebra. Moreover, the deRham approach to topology gives only real coefficients and neglects the torsion part.
– Piotr Hajlasz
5 hours ago




I know this book, but it does not really provides a good introduction to algebra. Moreover, the deRham approach to topology gives only real coefficients and neglects the torsion part.
– Piotr Hajlasz
5 hours ago




3




3




Ah! Probably I found the right textbook! Try to take a look at Topology and geometry-Bredon :) It covers the necessary algebra along the way and begins with the basic topics of Algebraic Topology.
– Vincenzo Zaccaro
5 hours ago






Ah! Probably I found the right textbook! Try to take a look at Topology and geometry-Bredon :) It covers the necessary algebra along the way and begins with the basic topics of Algebraic Topology.
– Vincenzo Zaccaro
5 hours ago




















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