The homotopy type of the PL cobordism category. II

2023/08/08 by Lopez, Mauricio Gomez
#57Q50 (Secondary) #57Q60 (Primary) #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2308.04612

Abstract

In this article, we prove the PL analogue of the theorem of Galatius, Madsen, Tillmann, and Weiss which describes the homotopy type of the smooth cobordism category. More specifically, we introduce the PL Madsen-Tillmann spectrum MTPL(d) and prove that there is a weak homotopy equivalence of the form BCob^PL_d ≃ Ω^∞-1MTPL(d). We also discuss how to adjust the methods of this paper to obtain the topological version of our main result.

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