The transfer map of free loop spaces
Authors:
John A. Lind and Cary Malkiewich
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
Published electronically:
November 27, 2018
MathSciNet review:
3896088
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Abstract | References | Similar Articles | Additional Information
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.
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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
Article copyright:
© Copyright 2018
American Mathematical Society