Higher index theory:
Index theory studies the solutions to differential equations on geometric spaces, their relation to the underlying geometry and topology, and applications to physics. If the space of solutions is infinite dimensional, it becomes necessary to generalise the classical Fredholm index using tools from t...
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| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2020
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| Schriftenreihe: | Cambridge studies in advanced mathematics
189 |
| Links: | https://doi.org/10.1017/9781108867351 |
| Zusammenfassung: | Index theory studies the solutions to differential equations on geometric spaces, their relation to the underlying geometry and topology, and applications to physics. If the space of solutions is infinite dimensional, it becomes necessary to generalise the classical Fredholm index using tools from the K-theory of operator algebras. This leads to higher index theory, a rapidly developing subject with connections to noncommutative geometry, large-scale geometry, manifold topology and geometry, and operator algebras. Aimed at geometers, topologists and operator algebraists, this book takes a friendly and concrete approach to this exciting theory, focusing on the main conjectures in the area and their applications outside of it. A well-balanced combination of detailed introductory material (with exercises), cutting-edge developments and references to the wider literature make this a valuable guide to this active area for graduate students and experts alike. |
| Umfang: | 1 Online-Ressource (xi, 581 Seiten) |
| ISBN: | 9781108867351 |
Internformat
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| 100 | 1 | |a Willett, Rufus |d 1983- | |
| 245 | 1 | 0 | |a Higher index theory |c Rufus Willett, Guoliang Yu |
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| 490 | 1 | |a Cambridge studies in advanced mathematics |v 189 | |
| 520 | |a Index theory studies the solutions to differential equations on geometric spaces, their relation to the underlying geometry and topology, and applications to physics. If the space of solutions is infinite dimensional, it becomes necessary to generalise the classical Fredholm index using tools from the K-theory of operator algebras. This leads to higher index theory, a rapidly developing subject with connections to noncommutative geometry, large-scale geometry, manifold topology and geometry, and operator algebras. Aimed at geometers, topologists and operator algebraists, this book takes a friendly and concrete approach to this exciting theory, focusing on the main conjectures in the area and their applications outside of it. A well-balanced combination of detailed introductory material (with exercises), cutting-edge developments and references to the wider literature make this a valuable guide to this active area for graduate students and experts alike. | ||
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| spelling | Willett, Rufus 1983- Higher index theory Rufus Willett, Guoliang Yu Cambridge Cambridge University Press 2020 1 Online-Ressource (xi, 581 Seiten) txt c cr Cambridge studies in advanced mathematics 189 Index theory studies the solutions to differential equations on geometric spaces, their relation to the underlying geometry and topology, and applications to physics. If the space of solutions is infinite dimensional, it becomes necessary to generalise the classical Fredholm index using tools from the K-theory of operator algebras. This leads to higher index theory, a rapidly developing subject with connections to noncommutative geometry, large-scale geometry, manifold topology and geometry, and operator algebras. Aimed at geometers, topologists and operator algebraists, this book takes a friendly and concrete approach to this exciting theory, focusing on the main conjectures in the area and their applications outside of it. A well-balanced combination of detailed introductory material (with exercises), cutting-edge developments and references to the wider literature make this a valuable guide to this active area for graduate students and experts alike. Yu, Guoliang 1963- Erscheint auch als Druck-Ausgabe 9781108491068 |
| spellingShingle | Willett, Rufus 1983- Higher index theory |
| title | Higher index theory |
| title_auth | Higher index theory |
| title_exact_search | Higher index theory |
| title_full | Higher index theory Rufus Willett, Guoliang Yu |
| title_fullStr | Higher index theory Rufus Willett, Guoliang Yu |
| title_full_unstemmed | Higher index theory Rufus Willett, Guoliang Yu |
| title_short | Higher index theory |
| title_sort | higher index theory |
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