Equivariant Principal ∞-Bundles
Cambridge University Press (Verlag)
978-1-009-69855-9 (ISBN)
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Principal bundles and their associated fiber bundles famously play a foundational role in both algebraic and differential topology, as well as in fundamental and solid-state physics. More recently, their equivariant and higher homotopy enhancements (gerbes) have been crucial in generalized cohomology theory and for the physics of extended solitons and topological phases. This text is the first to offer a unified perspective of, and introduction to, these topics, providing an insight into material previously scattered across the literature. After a self-contained account of the classical theory of equivariant principal bundles in modern topological groupoid language, the book develops, on the novel backdrop of cohesive higher topos theory, a powerful theory of equivariant principal higher bundles. It establishes new methods like the 'smooth Oka principle' and 'twisted Elmendorf theorem' to elegantly prove classification results and clarify the relation to proper equivariant generalized cohomology theories.
Hisham Sati is Professor of Mathematics at NYU Abu Dhabi and the founding director of the Center for Quantum and Topological Systems. His interdisciplinary research spans mathematical physics, algebraic topology, and differential geometry, and their interactions through fundamental physical theories. He has delivered the Adams Memorial Lecture in Topology. Together with Schreiber, he is coauthor of the monograph 'The Character Map in Non-Abelian Cohomology' (2023) and co-editor of the AMS collection 'Mathematical Foundations of Quantum Field and Perturbative String Theory' (2011). Urs Schreiber is Research Scientist at NYU Abu Dhabi, specializing in the mathematical foundations of quantum field theory. His work applies algebraic topology and geometric homotopy theory to fundamental physics, including topological quantum technology. He is a cocreator of the nLab, a research wiki for math and physics. Together with Sati, he is coauthor of the monograph 'The Character Map in Non-Abelian Cohomology' (2023) and co-editor of the AMS collection 'Mathematical Foundations of Quantum Field and Perturbative String Theory' (2011).
What this book is about; Part I. Introduction: 1. Introduction; Part II. In Topological Spaces: 2. Equivariant topology; 3. Equivariant principal bundles; Part III. In Cohesive ∞-Stacks: 4. Equivariant ∞-topos theory; 5. Equivariant principal ∞-bundles; Part IV. Examples and Applications: 6. Examples and applications; References; Index.
| Erscheint lt. Verlag | 30.6.2026 |
|---|---|
| Reihe/Serie | Cambridge Studies in Advanced Mathematics |
| Zusatzinfo | Worked examples or Exercises |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre | |
| ISBN-10 | 1-009-69855-9 / 1009698559 |
| ISBN-13 | 978-1-009-69855-9 / 9781009698559 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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