The transfer map of free loop spaces

2016/04/11 by Lind, John A., Malkiewich, Cary
#16E40 #19D55 #55M05 #55R12 #Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1604.03067

Abstract

For any perfect fibration E → B, there is a "free loop transfer map" LB₊ → LE₊, defined using topological Hochschild homology. We prove that this transfer is compatible with the Becker-Gottlieb transfer, allowing us to extend a result of Dorabiała and Johnson on the transfer map in Waldhausen's A-theory. In the case where E → B is a smooth fiber bundle, we also give a concrete geometric model for the free loop transfer in terms of Pontryagin-Thom collapse maps. We recover the previously known computations of the free loop transfer due to Schlichtkrull, and make a few new computations as well.

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