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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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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


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
  • © Copyright 2018 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 371 (2019), 2503-2552
  • MSC (2010): Primary 55R12; Secondary 19D10, 19D55, 55J35
  • DOI:
  • MathSciNet review: 3896088