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Koszul A∞-algebras and free loop space homology

Part of: Rings and algebras arising under various constructions Homotopy theory

Published online by Cambridge University Press:  18 July 2019

Alexander Berglund  and
Kaj Börjeson
Alexander Berglund
Affiliation:
Department of Mathematics, Stockholm University, SE-106 91 Stockholm, Sweden ([email protected])
Kaj Börjeson
Affiliation:
Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark ([email protected])
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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.

Keywords

Koszul dualityloop spacesA∞ algebras

MSC classification

Primary: 55P50: String topology 16S37: Quadratic and Koszul algebras
Secondary: 55P35: Loop spaces
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 63 , Issue 1 , February 2020 , pp. 37 - 65
Copyright
Copyright © Edinburgh Mathematical Society 2019

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