2016/01/15 by Stephan Mescher, Mescher, Stephan
Mathematics · #16E40 #FOS: Mathematics #Geometric Topology (math.GT) #Rings and Algebras (math.RA) #Symplectic Geometry (math.SG) #math.GT #math.RA #math.SG #msc:16E40
paper · pdf · doi:10.48550/arxiv.1601.03963
60 pages. Comments welcome
arxiv created 2016/01/15 · arxiv updated 2016/01/26
We present an elementary and self-contained construction of A_∞-algebras, A_∞-bimodules and their Hochschild homology and cohomology groups. In addition, we discuss the cup product in Hochschild cohomology and the spectral sequence of the length filtration of a Hochschild chain complex. A_∞-structures arise naturally in the study of based loop spaces and the geometry of manifolds, in particular in Lagrangian Floer theory and Morse homology. In several geometric situations, Hochschild homology may be used to describe homology groups of free loop spaces. The objective of this article is not to introduce new material, but to give a unified and coherent discussion of algebraic results from several sources. It further includes detailed proofs of all presented results.