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arXiv · 1905.10991

The homotopy invariance of cyclic homology of $A_\infty$-algebras over rings

S. V. Lapin
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Abstract

In the present paper the cyclic homology functor from the category of $A_\infty$-algebras over any commutative unital ring $K$ to the category of graded $K$-modules is constructed. Further, it is showed that this functor sends homotopy equivalences of $A_\infty$-algebras into isomorphisms of graded modules. As a corollary, it is obtained that the cyclic homology of an $A_\infty$-algebra over any field is isomorphic to the cyclic homology of the $A_\infty$-algebra of homologies for the source $A_\infty$-algebra.

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S. V. Lapin. 2019-05-27. The homotopy invariance of cyclic homology of $A_\infty$-algebras over rings. https://arxiv.org/abs/1905.10991

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