Global Homotopy Theory (New Mathematical Monographs)
Cambridge University Press, 9/6/2018
EAN 9781108425810, ISBN10: 110842581X
Hardcover, 846 pages, 23.5 x 15.8 x 4.6 cm
Language: English
Equivariant homotopy theory started from geometrically motivated questions about symmetries of manifolds. Several important equivariant phenomena occur not just for a particular group, but in a uniform way for all groups. Prominent examples include stable homotopy, K-theory or bordism. Global equivariant homotopy theory studies such uniform phenomena, i.e. universal symmetries encoded by simultaneous and compatible actions of all compact Lie groups. This book introduces graduate students and researchers to global equivariant homotopy theory. The framework is based on the new notion of global equivalences for orthogonal spectra, a much finer notion of equivalence than is traditionally considered. The treatment is largely self-contained and contains many examples, making it suitable as a textbook for an advanced graduate class. At the same time, the book is a comprehensive research monograph with detailed calculations that reveal the intrinsic beauty of global equivariant phenomena.
1. Unstable global homotopy theory
2. Ultra-commutative monoids
3. Equivariant stable homotopy theory
4. Global stable homotopy theory
5. Ultra-commutative ring spectra
6. Global Thom and K-theory spectra
Appendix A. Compactly generated spaces
Appendix B. Equivariant spaces
Appendix C. Enriched functor categories
Bibliography
Symbol Index
Index.