String operations on rational Gorenstein spaces

2013/01/09 by Takahito Naito, Naito, Takahito
Mathematics · #55P35 (Primary) 55P62 (Secondary) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1301.1785

openalex publication_date 2013/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Félix and Thomas developed string topology of Chas and Sullivan on simply-connected Gorenstein spaces. In this paper, we prove that the degree shifted homology of the free loop space of a simply-connected \mathbb Q-Gorenstein space with rational coefficient is a non-unital and non-counital Frobenius algebra by solving the up to constant problem. We also investigate triviality or non-triviality of the loop product and coproduct of particular Gorenstein spaces.

Citations

• A polarized view of string topology
• String topology of classifying spaces

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