Formal Geometry and Bordism Operations (Cambridge Studies in Advanced Mathematics)

Peterson, Eric

Cambridge University Press（2018/12発売）

• 製本 Hardcover:ハードカバー版／ページ数 418 p.
• 言語 ENG
• 商品コード 9781108428033
• DDC分類 514.24

Full Description

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.

Contents

Foreword Matthew Ando; Preface; Introduction; 1. Unoriented bordism; 2. Complex bordism; 3. Finite spectra; 4. Unstable cooperations; 5. The σ-orientation; Appendix A. Power operations; Appendix B. Loose ends; References; Index.