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Koszul A-algebras and free loop space homology

Published online by Cambridge University Press:  18 July 2019

Alexander Berglund
Affiliation:
Department of Mathematics, Stockholm University, SE-106 91 Stockholm, Sweden (alexb@math.su.se)
Kaj Börjeson
Affiliation:
Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark (kajb@math.ku.dk)

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.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2019

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