Formal Geometry and Bordism Operations
Published on 6. December 2018
Book
Hardback
418 pages
978-1-108-42803-3 (ISBN)
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.
Reviews / Votes
'It has a down-to-earth and inviting style (no small achievement in a book about functorial algebraic geometry). It is elegant, precise, and incisive, and it is strong on both theory and calculation.' Michael Berg, MAA Reviews 'This book is likely to be quite useful to graduate students in algebraic topology. For years it has been an informal tradition for students of algebraic topology to teach themselves enough of the foundations of algebraic geometry to be able to translate between theorems about Hopf algebroids and theorems about algebraic stacks, and then to proceed to translate, as much as possible, calculations and theorems in algebraic topology into equivalent formulations in terms of moduli stacks of formal groups and related objects. This book does a great service to such students (and their advisors!), as it gives good answers to many of the questions such students inevitably ask.' Andrew Salch, MatSciNet 'The presentation is lucid, pedagogical, and also offers a fresh point of view on classical topics. It draws from several mostly unpublished sources, for instance Strickland's manuscripts or various sets of notes by Goerss, Hopkins, and Lurie, and combines them in a single uniform treatment. Moreover, it contains a wealth of references to the published and unpublished literature that guides the interested reader to further topics that are only discussed in passing.' Tobias Barthel, zbMATH OpenMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
College/higher education
Illustrations
Worked examples or Exercises; 2 Plates, color; 2 Halftones, color; 6 Halftones, black and white; 9 Line drawings, black and white
Dimensions
Height: 235 mm
Width: 157 mm
Thickness: 27 mm
Weight
756 gr
ISBN-13
978-1-108-42803-3 (9781108428033)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Eric Peterson
Formal Geometry and Bordism Operations
E-Book
12/2018
Cambridge University Press
€76.99
Available for download
Person
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.
Content
Foreword Matthew Ando; Preface; Introduction; 1. Unoriented bordism; 2. Complex bordism; 3. Finite spectra; 4. Unstable cooperations; 5. The ?-orientation; Appendix A. Power operations; Appendix B. Loose ends; References; Index.