Massey Product and Twisted Cohomology of A-infinity Algebras

Details Massey Product and Twisted Cohomology of A-infinity Algebras Massey Product and Twisted Cohomology of A-infinity Algebras

2009-12-09

arxiv.org/abs/0912.1775v2

Mathematics

Algebraic Topology

32 pages

Scientific paper

We study the twisted cohomology groups of $A_\infty$-algebras defined by twisting elements and their behavior under morphisms and homotopies using the bar construction. We define higher Massey products on the cohomology groups of general $A_\infty$-algebras and establish the naturality under morphisms and their dependency on defining systems. The above constructions are also considered for $C_\infty$-algebras. We construct a spectral sequence converging to the twisted cohomology groups an show that the higher differentials are given by the $A_\infty$-algebraic Massey products.

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