Complexo de cadeias

Multi tool use
Multi tool use




Em topologia algébrica e em álgebra homológica, um complexo de cadeias é uma sequência de grupos abelianos e homomorfismos


⋯→An+1→dn+1An→dnAn−1→dn−1An−2→⋯→d2A1→d1A0→d0A−1→d−1A−2→d−2⋯{displaystyle cdots to A_{n+1}{xrightarrow {d_{n+1}}}A_{n}{xrightarrow {d_{n}}}A_{n-1}{xrightarrow {d_{n-1}}}A_{n-2}to cdots {xrightarrow {d_{2}}}A_{1}{xrightarrow {d_{1}}}A_{0}{xrightarrow {d_{0}}}A_{-1}{xrightarrow {d_{-1}}}A_{-2}{xrightarrow {d_{-2}}}cdots }{displaystyle cdots to A_{n+1}{xrightarrow {d_{n+1}}}A_{n}{xrightarrow {d_{n}}}A_{n-1}{xrightarrow {d_{n-1}}}A_{n-2}to cdots {xrightarrow {d_{2}}}A_{1}{xrightarrow {d_{1}}}A_{0}{xrightarrow {d_{0}}}A_{-1}{xrightarrow {d_{-1}}}A_{-2}{xrightarrow {d_{-2}}}cdots }

tais que dn∘dn+1=0{displaystyle d_{n}circ d_{n+1}=0}{displaystyle d_{n}circ d_{n+1}=0}.




Os complexos de cadeias fazem parte da definição dos grupos de homologia.





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