Brace algebras and the cohomology comparison theorem

2001/12/18 by Patras, F.
#16E40 #18D50 #55N10 #55P48 #Algebraic Topology (math.AT) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.math/0112177

Abstract

The Gerstenhaber and Schack cohomology comparison theorem asserts that there is a cochain equivalence between the Hochschild complex of a certain algebra and the usual singular cochain complex of a space. We show that this comparison theorem preserves the brace algebra structures. This result gives a structural reason for the recent results establishing fine topological structures on the Hochschild cohomology, and a simple way to derive them from the corresponding properties of cochain complexes.

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