## The transfer map of free loop spaces

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- by John A. Lind and Cary Malkiewich PDF
- Trans. Amer. Math. Soc.
**371**(2019), 2503-2552 Request permission

## Abstract:

For any perfect fibration $E \longrightarrow B$, there is a “free loop transfer map” $LB_+ \longrightarrow LE_+$, 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 $E \longrightarrow B$ 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.## References

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## Additional Information

**John A. Lind**- Affiliation: Department of Mathematics, Reed College, Portland, Oregon 97202
- MR Author ID: 1028377
**Cary Malkiewich**- Affiliation: Department of Mathematical Sciences, Binghamton University, Binghamton, New York 13902-6000
- MR Author ID: 1112752
- Received by editor(s): May 19, 2016
- Received by editor(s) in revised form: August 27, 2017
- Published electronically: November 27, 2018
- Additional Notes: The first author was partially supported by the DFG through SFB1085

The second author was partially supported by an AMS Simons Travel Grant - © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**371**(2019), 2503-2552 - MSC (2010): Primary 55R12; Secondary 19D10, 19D55, 55J35
- DOI: https://doi.org/10.1090/tran/7497
- MathSciNet review: 3896088