Formal Geometry and Bordism Operations

Erscheinungsjahr 2019
ISBN: 978-1-108-42803-3
Verlag: Cambridge University Press

Buch, Englisch, Band 177, 418 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 756 g

Reihe: Cambridge Studies in Advanced Mathematics

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.

Autoren/Hrsg.

Peterson, Eric

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie

Inhaltsverzeichnis

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.

Über Autor(innen)

Peterson, Eric
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.