Equivariant stable homotopy theory
Stefan Schwede
- 01 Sep 2018
- pp 227-347
TL;DR: In this article, the authors introduce graduate students and researchers to global equivariant homotopy theory based on the new notion of global equivalences for orthogonal spectra, a much finer notion of equivalence than what is traditionally considered.
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Abstract: 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 what 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.
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Charles A. Weibel
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TL;DR: The landscape of homological algebra has evolved over the last half-century into a fundamental tool for the working mathematician as discussed by the authors, which is suitable for second or third year graduate students.
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C*-Algebras and Operator Theory
Gerard J. Murphy
- 11 Sep 1990
TL;DR: Theory of C*-Algebras and Hilbert Space Operators Ideals and Positive Functionals Von Neumann Algebra Representations of C *-Algebra Direct Limits and Tensor Products K-Theory as discussed by the authors.
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