Formal Geometry and Bordism Operations
Seiten
2018
Cambridge University Press (Verlag)
978-1-108-42803-3 (ISBN)
Cambridge University Press (Verlag)
978-1-108-42803-3 (ISBN)
This is the first book to provide a broad, conceptual introduction to the field of chromatic homotopy, an active area of current research. It will be useful for graduate students interested in modern developments in algebraic topology and their links to other fields, including algebraic geometry and mathematical physics.
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.
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.
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.
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.
| Erscheinungsdatum | 07.12.2018 |
|---|---|
| Reihe/Serie | Cambridge Studies in Advanced Mathematics |
| Zusatzinfo | Worked examples or Exercises; 2 Plates, color; 2 Halftones, color; 6 Halftones, black and white; 9 Line drawings, black and white |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 157 x 234 mm |
| Gewicht | 790 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre | |
| Naturwissenschaften ► Physik / Astronomie | |
| ISBN-10 | 1-108-42803-7 / 1108428037 |
| ISBN-13 | 978-1-108-42803-3 / 9781108428033 |
| Zustand | Neuware |
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