FORMAL GEOMETRY AND BORDISM OPERATIONS

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

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.

Features
• 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

Author
Eric Peterson, Harvard University, Massachusetts
Eric Peterson works in quantum compilation for near-term supremacy hardware at Rigetti Computing in Berkeley, California. He was previously a Benjamin Peirce Fellow at Harvard University.