Transfer in generalized cohomology theories (Q2707381)

The book under review essentially coincides with the author's 1971 Princeton thesis, which is an early influential account on transfer in generalized cohomology theories. The concept of transfer has been used in topology long before, and it was only in the beginning of the seventies that various topologists independently realized that transfer actually can be described by a stable map. One of the first articles where such a stable transfer map is defined is [Bull. Am. Math. Soc. 78, 981-987 (1972; Zbl 0265.55009)] by \textit{D. S. Kahn} and \textit{S. B. Priddy} who also mention the author's work; however, for some reason the author's thesis did not get published at that time.NEWLINENEWLINENEWLINEProbably the most important two aspects of the author's thesis were the actual definition of the stable transfer map and the axiomatic characterization of the latter. In addition the author derived various properties of the transfer in generalized cohomology theories and studied the relations between transfer and Dyer-Lashof operations. Quite a substantial part of the thesis also is on additional properties of the transfer that only hold for specified generalized cohomology theories as e.g.~for singular cohomology or for K-theory.NEWLINENEWLINENEWLINEThe book (resp.~the thesis) is organized as follows. After the introduction there are three chapters that review relevant material on coverings and fiber bundles as well as on the category of spectra and on generalized cohomology theories. In the following chapter the author collects what was known about the classical transfer in singular cohomology, K-theory and in cobordism theory. The next three chapters contain the author's general approach to the transfer, and the remaining six chapters are dealing with various properties of the generalized transfer. Finally, there also is an appendix added to the original account by the author in which he summarizes the developments that have been taken place within this field from then until now.