Koszul A-infinity algebras and free loop space homology

2017/11/17 by Alexander Berglund, Berglund, Alexander, Kaj Börjeson +1
Mathematics · #16E40 #16S37 Secondary: 55P35 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary: 55P50 #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1711.06496

openalex publication_date 2017/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a notion of Koszul A-infinity algebra that generalizes Priddy's notion of a Koszul algebra and we use it to construct small A-infinity 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.

Citations

• Higher string topology operations

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