nLab
Becker-Gottlieb transfer

Context

Cohomology

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

Contents

Idea

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.

Definition

See e.g. (Haugseng 13, def. 3.9).

References

The original article is

(which also gives a proof of the Adams conjecture).

Reviews include

Discussion in the context of differential algebraic K-theory is in

In prop. 4.14 of

Becker-Gottlieb transfer was identified with the Umkehr map induced from a Wirthmüller context in which in addition f *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 March 8, 2016 at 16:37:39. See the history of this page for a list of all contributions to it.