Formal Geometry and Bordism Operations: 177 (Cambridge Studies in Advanced Mathematics, Series Number 177)
Cambridge University Press, 12/6/2018
EAN 9781108428033, ISBN10: 1108428037
Hardcover, 418 pages, 23.4 x 15.7 x 2.3 cm
Language: English
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.
Foreword Matthew Ando
Preface
Introduction
1. Unoriented bordism
2. Complex bordism
3. Finite spectra
4. Unstable cooperations
5. The ÃÆ’-orientation
Appendix A. Power operations
Appendix B. Loose ends
References
Index.