Relative index theory, determinants and torsion for open manifolds:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Singapore
World Scientific Pub. Co.
©2009
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| Schlagwörter: | |
| Links: | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=305154 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=305154 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=305154 |
| Beschreibung: | Includes bibliographical references (pages 331-337) and index Introduction -- I. Absolute invariants for open manifolds and bundles. 1. Absolute characteristic numbers. 2. Index theorems for open manifolds -- II. Non-linear Sobolev structures. 1. Clifford bundles, generalized Dirac operators and associated Sobolev spaces. 2. Uniform structures of metric spaces. 3. Completed manifolds of maps. 4. Uniform structures of manifolds and Clifford bundles. 5. The classification problem, new (co- )homologies and relative characteristic numbers -- III. The heat kernel of generalized Dirac operators. 1. Invariance properties of the spectrum and the heat kernel. 2. Duhamel's principle, scattering theory and trace class conditions -- IV. Trace class properties. 1. Variation of the Clifford connection. 2. Variation of the Clifford structure. 3. Additional topological perturbations -- V. Relative index theory. 1. Relative index theorems, the spectral shift function and the scattering index -- VI. Relative [symbol]-functions, [symbol]-functions, determinants and torsion. 1. Pairs of asymptotic expansions. 2. Relative [symbol]-functions. 3. Relative determinants and QFT. 4. Relative analytic torsion. 5. Relative [symbol]-invariants. 6. Examples and applications -- VII. Scattering theory for manifolds with injectivity radius zero. 1. Uniform structures defined by decay functions. 2. The injectivity radius and weighted Sobolev spaces. 3. Mapping properties of e[symbol]. 4. Proof of the trace class property -- References -- List of notations -- Index For closed manifolds, there is a highly elaborated theory of number-valued invariants, attached to the underlying manifold, structures and differential operators. On open manifolds, nearly all of this fails, with the exception of some special classes. The goal of this monograph is to establish for open manifolds, structures and differential operators an applicable theory of number-valued relative invariants. This is of great use in the theory of moduli spaces for nonlinear partial differential equations and mathematical physics. The book is self-contained: in particular, it contains an outline of the necessary tools from nonlinear Sobolev analysis |
| Umfang: | 1 Online-Ressource (x, 341 pages) |
| ISBN: | 9789812771445 9789812771452 9812771441 981277145X |
Internformat
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| 245 | 1 | 0 | |a Relative index theory, determinants and torsion for open manifolds |c Jürgen Eichhorn |
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| 500 | |a Includes bibliographical references (pages 331-337) and index | ||
| 500 | |a Introduction -- I. Absolute invariants for open manifolds and bundles. 1. Absolute characteristic numbers. 2. Index theorems for open manifolds -- II. Non-linear Sobolev structures. 1. Clifford bundles, generalized Dirac operators and associated Sobolev spaces. 2. Uniform structures of metric spaces. 3. Completed manifolds of maps. 4. Uniform structures of manifolds and Clifford bundles. 5. The classification problem, new (co- )homologies and relative characteristic numbers -- III. The heat kernel of generalized Dirac operators. 1. Invariance properties of the spectrum and the heat kernel. 2. Duhamel's principle, scattering theory and trace class conditions -- IV. Trace class properties. 1. Variation of the Clifford connection. 2. Variation of the Clifford structure. 3. Additional topological perturbations -- V. Relative index theory. 1. Relative index theorems, the spectral shift function and the scattering index -- VI. Relative [symbol]-functions, [symbol]-functions, determinants and torsion. 1. Pairs of asymptotic expansions. 2. Relative [symbol]-functions. 3. Relative determinants and QFT. 4. Relative analytic torsion. 5. Relative [symbol]-invariants. 6. Examples and applications -- VII. Scattering theory for manifolds with injectivity radius zero. 1. Uniform structures defined by decay functions. 2. The injectivity radius and weighted Sobolev spaces. 3. Mapping properties of e[symbol]. 4. Proof of the trace class property -- References -- List of notations -- Index | ||
| 500 | |a For closed manifolds, there is a highly elaborated theory of number-valued invariants, attached to the underlying manifold, structures and differential operators. On open manifolds, nearly all of this fails, with the exception of some special classes. The goal of this monograph is to establish for open manifolds, structures and differential operators an applicable theory of number-valued relative invariants. This is of great use in the theory of moduli spaces for nonlinear partial differential equations and mathematical physics. The book is self-contained: in particular, it contains an outline of the necessary tools from nonlinear Sobolev analysis | ||
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Datensatz im Suchindex
| _version_ | 1818981234436472832 |
|---|---|
| any_adam_object | |
| author | Eichhorn, Jürgen 1942- |
| author_GND | (DE-588)1049961633 |
| author_facet | Eichhorn, Jürgen 1942- |
| author_role | aut |
| author_sort | Eichhorn, Jürgen 1942- |
| author_variant | j e je |
| building | Verbundindex |
| bvnumber | BV043098408 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)613678168 (DE-599)BVBBV043098408 |
| dewey-full | 516.36 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.36 |
| dewey-search | 516.36 |
| dewey-sort | 3516.36 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043098408 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:28:05Z |
| institution | BVB |
| isbn | 9789812771445 9789812771452 9812771441 981277145X |
| language | English |
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| owner_facet | DE-1046 DE-1047 |
| physical | 1 Online-Ressource (x, 341 pages) |
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| publishDate | 2009 |
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| publisher | World Scientific Pub. Co. |
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| spelling | Eichhorn, Jürgen 1942- Verfasser (DE-588)1049961633 aut Relative index theory, determinants and torsion for open manifolds Jürgen Eichhorn Singapore World Scientific Pub. Co. ©2009 1 Online-Ressource (x, 341 pages) txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references (pages 331-337) and index Introduction -- I. Absolute invariants for open manifolds and bundles. 1. Absolute characteristic numbers. 2. Index theorems for open manifolds -- II. Non-linear Sobolev structures. 1. Clifford bundles, generalized Dirac operators and associated Sobolev spaces. 2. Uniform structures of metric spaces. 3. Completed manifolds of maps. 4. Uniform structures of manifolds and Clifford bundles. 5. The classification problem, new (co- )homologies and relative characteristic numbers -- III. The heat kernel of generalized Dirac operators. 1. Invariance properties of the spectrum and the heat kernel. 2. Duhamel's principle, scattering theory and trace class conditions -- IV. Trace class properties. 1. Variation of the Clifford connection. 2. Variation of the Clifford structure. 3. Additional topological perturbations -- V. Relative index theory. 1. Relative index theorems, the spectral shift function and the scattering index -- VI. Relative [symbol]-functions, [symbol]-functions, determinants and torsion. 1. Pairs of asymptotic expansions. 2. Relative [symbol]-functions. 3. Relative determinants and QFT. 4. Relative analytic torsion. 5. Relative [symbol]-invariants. 6. Examples and applications -- VII. Scattering theory for manifolds with injectivity radius zero. 1. Uniform structures defined by decay functions. 2. The injectivity radius and weighted Sobolev spaces. 3. Mapping properties of e[symbol]. 4. Proof of the trace class property -- References -- List of notations -- Index For closed manifolds, there is a highly elaborated theory of number-valued invariants, attached to the underlying manifold, structures and differential operators. On open manifolds, nearly all of this fails, with the exception of some special classes. The goal of this monograph is to establish for open manifolds, structures and differential operators an applicable theory of number-valued relative invariants. This is of great use in the theory of moduli spaces for nonlinear partial differential equations and mathematical physics. The book is self-contained: in particular, it contains an outline of the necessary tools from nonlinear Sobolev analysis MATHEMATICS / Geometry / Differential bisacsh Manifolds (Mathematics) Index theory (Mathematics) Torsionstheorie (DE-588)4451084-6 gnd rswk-swf Determinante (DE-588)4138983-9 gnd rswk-swf Indextheorie (DE-588)4161489-6 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 s Indextheorie (DE-588)4161489-6 s Torsionstheorie (DE-588)4451084-6 s Determinante (DE-588)4138983-9 s 1\p DE-604 World Scientific (Firm) Sonstige oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=305154 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Eichhorn, Jürgen 1942- Relative index theory, determinants and torsion for open manifolds MATHEMATICS / Geometry / Differential bisacsh Manifolds (Mathematics) Index theory (Mathematics) Torsionstheorie (DE-588)4451084-6 gnd Determinante (DE-588)4138983-9 gnd Indextheorie (DE-588)4161489-6 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd |
| subject_GND | (DE-588)4451084-6 (DE-588)4138983-9 (DE-588)4161489-6 (DE-588)4037379-4 |
| title | Relative index theory, determinants and torsion for open manifolds |
| title_auth | Relative index theory, determinants and torsion for open manifolds |
| title_exact_search | Relative index theory, determinants and torsion for open manifolds |
| title_full | Relative index theory, determinants and torsion for open manifolds Jürgen Eichhorn |
| title_fullStr | Relative index theory, determinants and torsion for open manifolds Jürgen Eichhorn |
| title_full_unstemmed | Relative index theory, determinants and torsion for open manifolds Jürgen Eichhorn |
| title_short | Relative index theory, determinants and torsion for open manifolds |
| title_sort | relative index theory determinants and torsion for open manifolds |
| topic | MATHEMATICS / Geometry / Differential bisacsh Manifolds (Mathematics) Index theory (Mathematics) Torsionstheorie (DE-588)4451084-6 gnd Determinante (DE-588)4138983-9 gnd Indextheorie (DE-588)4161489-6 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd |
| topic_facet | MATHEMATICS / Geometry / Differential Manifolds (Mathematics) Index theory (Mathematics) Torsionstheorie Determinante Indextheorie Mannigfaltigkeit |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=305154 |
| work_keys_str_mv | AT eichhornjurgen relativeindextheorydeterminantsandtorsionforopenmanifolds AT worldscientificfirm relativeindextheorydeterminantsandtorsionforopenmanifolds |