# A primer on A-infinity-algebras and their Hochschild homology

@article{Mescher2016APO, title={A primer on A-infinity-algebras and their Hochschild homology}, author={Stephan Mescher}, journal={arXiv: Rings and Algebras}, year={2016} }

We present an elementary and self-contained construction of $A_\infty$-algebras, $A_\infty$-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.
$A_\infty$-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… CONTINUE READING

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