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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| Hauptverfasser: | , |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
[2020]
|
| Schriftenreihe: | Cambridge studies in advanced mathematics
189 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBA01 UPA01 Volltext |
| 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 |
| Beschreibung: | 1 Online-Ressource (xi, 581 Seiten) |
| ISBN: | 9781108867351 |
| DOI: | 10.1017/9781108867351 |
Internformat
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| 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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| discipline | Mathematik |
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| illustrated | Not Illustrated |
| index_date | 2024-07-03T15:00:09Z |
| indexdate | 2024-07-10T08:54:37Z |
| institution | BVB |
| isbn | 9781108867351 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032224351 |
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| physical | 1 Online-Ressource (xi, 581 Seiten) |
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| publishDate | 2020 |
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| publisher | Cambridge University Press |
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| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Willett, Rufus 1983- Verfasser (DE-588)1212441923 aut Higher index theory Rufus Willett, Guoliang Yu Cambridge Cambridge University Press [2020] © 2020 1 Online-Ressource (xi, 581 Seiten) txt rdacontent c rdamedia cr rdacarrier 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 Index theory (Mathematics) C*-algebras K-theory K-Theorie (DE-588)4033335-8 gnd rswk-swf Indextheorie (DE-588)4161489-6 gnd rswk-swf Indextheorie (DE-588)4161489-6 s K-Theorie (DE-588)4033335-8 s DE-604 Yu, Guoliang 1963- Verfasser (DE-588)1026997461 aut Erscheint auch als Druck-Ausgabe, Hardcover 978-1-108-49106-8 Cambridge studies in advanced mathematics 189 (DE-604)BV044781283 189 https://doi.org/10.1017/9781108867351 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Willett, Rufus 1983- Yu, Guoliang 1963- Higher index theory Cambridge studies in advanced mathematics Index theory (Mathematics) C*-algebras K-theory K-Theorie (DE-588)4033335-8 gnd Indextheorie (DE-588)4161489-6 gnd |
| subject_GND | (DE-588)4033335-8 (DE-588)4161489-6 |
| title | Higher index theory |
| title_auth | Higher index theory |
| title_exact_search | Higher index theory |
| title_exact_search_txtP | 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 |
| topic | Index theory (Mathematics) C*-algebras K-theory K-Theorie (DE-588)4033335-8 gnd Indextheorie (DE-588)4161489-6 gnd |
| topic_facet | Index theory (Mathematics) C*-algebras K-theory K-Theorie Indextheorie |
| url | https://doi.org/10.1017/9781108867351 |
| volume_link | (DE-604)BV044781283 |
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