Corpus ID: 119664925

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

  title={A primer on A-infinity-algebras and their Hochschild homology},
  author={Stephan Mescher},
  journal={arXiv: Rings and Algebras},
  • Stephan Mescher
  • Published 2016
  • Mathematics
  • arXiv: Rings and Algebras
  • 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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    Publications referenced by this paper.

    A∞-structures associated to Lefschetz fibrations

    • Fukaya
    • I, J. Symplectic Geom
    • 2012

    A∞-subalgebras and natural transformations, Homology

    • Paul Seidel
    • Homotopy Appl
    • 2008

    A user’s guide to spectral sequences, second ed

    • John McCleary
    • Cambridge Studies in Advanced Mathematics,
    • 2001

    A∞ algebras and the cohomology of moduli spaces, Lie groups and Lie algebras: E

    • Michael Penkava, Albert Schwarz
    • B. Dynkin’s Seminar, Amer. Math. Soc. Transl. Ser. 2,
    • 1995