Math 549.
Topic in algebraic
topology
Spring, 2015.
There will be two main topics in this course:
- Foundations of stable homotopy theory. We will look at various
definitions of spectra, both ordinary and equivariant. Here are soome references for this topic, in chronological order.
- Stable homotopy and generalised homology
(Google Books link) by J. F. Adams, 1971
- Equivariant Stable Homotopy Theory
by G. Lewis,
J. P. May, and M. Steinberger, 1985
- RINGS, MODULES, AND ALGEBRAS IN STABLE HOMOTOPY THEORY by A. D. Elmendorf, I. Kriz, M. A. Mandell, and
J. P. May, 1997.
- EQUIVARIANT ORTHOGONAL SPECTRA by M.A. Mandell and J.P. May, 2002.
- ON THE NON-EXISTENCE OF ELEMENTS OF KERVAIRE INVARIANT
ONE, Appendices A and B, by M. A. Hill, M. J. Hopkins and D. C
Ravenel, to appear.
- Computational methods, mostly involving spectral sequences. Refernces will be supplied later.