Koszul A∞-algebras and free loop space homology

Alexander Berglund; Kaj Börjeson

doi:10.1017/S0013091519000154

Koszul A_∞-algebras and free loop space homology

Alexander Berglund^*, Kaj Börjeson

^*Corresponding author af dette arbejde

Institut for Matematiske Fag

Abstract

We introduce a notion of Koszul A-algebra that generalizes Priddy's notion of a Koszul algebra and we use it to construct small A-algebra models for Hochschild cochains. As an application, this yields new techniques for computing free loop space homology algebras of manifolds that are either formal or coformal (over a field or over the integers). We illustrate these techniques in two examples.

Originalsprog	Engelsk
Tidsskrift	Proceedings of the Edinburgh Mathematical Society
Antal sider	29
ISSN	0013-0915
DOI	https://doi.org/10.1017/S0013091519000154
Status	Udgivet - 1 feb. 2020

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10.1017/S0013091519000154

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Link to publication in Scopus

Citationsformater

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AB - We introduce a notion of Koszul A-algebra that generalizes Priddy's notion of a Koszul algebra and we use it to construct small A-algebra models for Hochschild cochains. As an application, this yields new techniques for computing free loop space homology algebras of manifolds that are either formal or coformal (over a field or over the integers). We illustrate these techniques in two examples.

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KW - loop spaces

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