Evaluation maps and transfers for free loop spaces II

2021/09/28 by Sune Precht Reeh, Reeh, Sune Precht, Tomer M. Schlank +3
Mathematics · #19A22 #55P35 #55R12 #55R37 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2109.13988

openalex publication_date 2021/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In our previous paper, we constructed and studied a functorial extension of the evaluation map S¹ × LX → X to transfers along finite covers. In this paper, we show that this induces a natural evaluation map on the full subcategory of the homotopy category of spectra consisting of p-completed classifying spectra of finite groups. To do this, we leverage the close relationship between this full subcategory and the Burnside category of fusion systems.

Citations

• Fusion systems and localities

Related

• Evaluation maps and transfers for free loop spaces I
• The subgroup homology decomposition for fusion systems is sharp
• Spectral enrichments of model categories
• Free loop spaces and the Cauchy--Frobenius Lemma
• Fundamental groups and descriptive set theory