The Transfer is Functorial
Abstract
We prove that the Becker-Gottlieb transfer is functorial up to homotopy, for all fibrations with finitely dominated fibers. This resolves a lingering foundational question about the transfer, which was originally defined in the late 1970s in order to simplify the proof of the Adams conjecture. Our approach differs from previous attempts in that we closely emulate the geometric argument in the case of a smooth fiber bundle. This leads to a "multiplicative'" description of the transfer, different from the standard presentation as the trace of a diagonal map.
Keywords
Cite
@article{arxiv.1603.01872,
title = {The Transfer is Functorial},
author = {John R. Klein and Cary Malkiewich},
journal= {arXiv preprint arXiv:1603.01872},
year = {2023}
}
Comments
This paper contains an error: the diagram (13) in the proof of Proposition 6.5 does not strictly commute as claimed. See https://doi.org/10.1016/j.aim.2022.108752 for more details. The authors would like to thank Shachar Carmeli and Bastiaan Cnossen for finding this error and bringing it to their attention