Formal Geometry and Bordism Operations
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- Author: Eric Peterson, Harvard University, Massachusetts
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This text organizes a range of results in chromatic homotopy theory, running a single thread through theorems in bordism and a detailed understanding of the moduli of formal groups. It emphasizes the naturally occurring algebro-geometric models that presage the topological results, taking the reader through a pedagogical development of the field. In addition to forming the backbone of the stable homotopy category, these ideas have found application in other fields: the daughter subject 'elliptic cohomology' abuts mathematical physics, manifold geometry, topological analysis, and the representation theory of loop groups. The common language employed when discussing these subjects showcases their unity and guides the reader breezily from one domain to the next, ultimately culminating in the construction of Witten's genus for String manifolds. This text is an expansion of a set of lecture notes for a topics course delivered at Harvard University during the spring term of 2016.Read more
- Gives graduate students the necessary information to conduct their own research without having to search through the literature
- Covers a broad range of material, presented in a way that makes cross-referencing easy for readers
- Prepares readers for cross-disciplinary work by bringing together many different fields of mathematics
Reviews & endorsements
'It has a down-to-earth and inviting style (no small achievement in a book about functorial algebraic geometry). It is elegant, precise, and incisive, and it is strong on both theory and calculation.' Michael Berg, MAA Reviews
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- Date Published: December 2018
- format: Adobe eBook Reader
- isbn: 9781108568067
- contains: 15 b/w illus. 4 colour illus.
- availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
Foreword Matthew Ando
1. Unoriented bordism
2. Complex bordism
3. Finite spectra
4. Unstable cooperations
5. The σ-orientation
Appendix A. Power operations
Appendix B. Loose ends
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