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arXiv · 1604.03067

The transfer map of free loop spaces

John A. Lind·Cary Malkiewich
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Abstract

For any perfect fibration $E \rightarrow B$, there is a "free loop transfer map" $LB_+ \rightarrow LE_+$, 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 $E \rightarrow B$ 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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John A. Lind, Cary Malkiewich. 2018-01-17. The transfer map of free loop spaces. https://arxiv.org/abs/1604.03067

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