group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
The Becker-Gottlieb transfer is a variant of push-forward in generalized cohomology of cohomology theories along proper submersions of smooth manifolds.
The Becker-Gottlieb transfer operation has been refined to differential cohomology in (Bunke-Gepner 13).
Its compatibility in differential algebraic K-theory with the differential refinement of the Borel regulator is the content of the transfer index conjecture (Bunke-Tamme 12, conjecture 1.1, Bunke-Gepner 13, conjecture 5.3).
For the moment see at regulator – Becker-Gottlieb transfer for more.
See e.g. (Haugseng 13, def. 3.9).
The original articles
James Becker, Daniel Gottlieb, The transfer map and fiber bundles, Topology , 14 (1975) (pdf, doi:10.1016/0040-9383(75)90029-4)
(which also gives a proof of the Adams conjecture).
James Becker, Daniel Gottlieb, Vector fields and transfers Manuscr. Math. , 72 (1991) pp. 111–130 (pdf, doi:10.1007/BF02568269)
Review:
Dai Tamaki, Akira Kono, Section 4.5 in: Generalized Cohomology, Translations of Mathematical Monographs, American Mathematical Society, 2006 (ISBN: 978-0-8218-3514-2)
Discussion in the context of differential algebraic K-theory is in
Ulrich Bunke, Georg Tamme, section 2.1 of Regulators and cycle maps in higher-dimensional differential algebraic K-theory (arXiv:1209.6451)
Ulrich Bunke, David Gepner, Differential function spectra, the differential Becker-Gottlieb transfer, and applications to differential algebraic K-theory (arXiv:1306.0247)
In prop. 4.14 of
Becker-Gottlieb transfer was identified with the Umkehr map induced from a Wirthmüller context in which in addition $f_\ast$ satisfies its projection formula (a “transfer context”, def.4.9)
The article
establishes the functoriality of the Becker-Gottlieb transfer for fibrations with finitely dominated fibers, but only on the level of homotopy categories (without higher coherences).
Last revised on January 3, 2021 at 02:12:05. See the history of this page for a list of all contributions to it.