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 for this work

Department of Mathematical Sciences

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.

Original language	English
Journal	Proceedings of the Edinburgh Mathematical Society
Number of pages	29
ISSN	0013-0915
DOIs	https://doi.org/10.1017/S0013091519000154
Publication status	Published - 1 Feb 2020

Keywords

A algebras
Koszul duality
loop spaces

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10.1017/S0013091519000154

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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.",

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AU - Börjeson, Kaj

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N2 - 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.

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 - Koszul duality

KW - loop spaces

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SN - 0013-0915

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JF - Proceedings of the Edinburgh Mathematical Society

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Koszul A_∞-algebras and free loop space homology

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Keywords

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