The Becker-Gottlieb Transfer Is Functorial

TL;DR

This paper proves that the Becker-Gottlieb transfer, a tool in algebraic topology, is functorial at the homotopy category level, clarifying its behavior for certain classes of space maps.

Contribution

It establishes the contravariant functoriality of the Becker-Gottlieb transfer on the homotopy category, extending its known properties.

Findings

The transfer is functorial on the homotopy category.

It applies to maps with homotopy fibers that are retracts of finite complexes.

Provides a new understanding of the transfer's structural properties.

Abstract

The Becker-Gottlieb transfer gives a wrong-way map on suspension spectra for maps of spaces whose homotopy fibres are retracts of finite complexes. We prove that this construction is contravariantly functorial on the homotopy category level.