Title: Functoriality of the Becker-Gottlieb Transfer
Speaker: Rune Haugseng (Max Planck Institute, Bonn)
Abstract: The Becker-Gottlieb transfer is a wrong-way map of suspension spectra that induces useful wrong-way maps in various (co)homology theories. Becker and Gottlieb gave two constructions of this transfer. The first, which relies on the Pontryagin-Thom construction, works for certain fibre bundles with compact manifold fibres, and is easily seen to be functorial. The second construction, in the most recent version due to May and Sigurdsson, gives a transfer for any continuous map whose homotopy fibres are retracts of finite CW-complexes, but it is not so obvious that this defines a functor. I will describe a purely homotopy-theoretical proof that this version of the transfer is also functorial.