Twisted Morse complexes: Morse homology and cohomology with local coefficients
1. Introduction -- 2. The Morse Complex with Local Coefficients -- 3. The Homology Determined by the Isomorphism Class of G -- 4. Singular and CW-Homology with Local Coefficients -- 5. Twisted Morse Cohomology and Lichnerowicz Cohomology -- 6. Applications and Computations.
Gespeichert in:
Hauptverfasser: | , , |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Cham, Switzerland
Springer
[2024]
|
Schriftenreihe: | Lecture notes in mathematics
Volume 2361 |
Zusammenfassung: | 1. Introduction -- 2. The Morse Complex with Local Coefficients -- 3. The Homology Determined by the Isomorphism Class of G -- 4. Singular and CW-Homology with Local Coefficients -- 5. Twisted Morse Cohomology and Lichnerowicz Cohomology -- 6. Applications and Computations. This book gives a detailed presentation of twisted Morse homology and cohomology on closed finite-dimensional smooth manifolds. It contains a complete proof of the Twisted Morse Homology Theorem, which says that on a closed finite-dimensional smooth manifold the homology of the Morse–Smale–Witten chain complex with coefficients in a bundle of abelian groups G is isomorphic to the singular homology of the manifold with coefficients in G. It also includes proofs of twisted Morse-theoretic versions of well-known theorems such as Eilenberg's Theorem, the Poincaré Lemma, and the de Rham Theorem. The effectiveness of twisted Morse complexes is demonstrated by computing the Lichnerowicz cohomology of surfaces, giving obstructions to spaces being associative H-spaces, and computing Novikov numbers. Suitable for a graduate level course, the book may also be used as a reference for graduate students and working mathematicians or physicists. |
Beschreibung: | viii, 155 Seiten Illustrationen, Diagramme |
ISBN: | 9783031716157 |
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245 | 1 | 0 | |a Twisted Morse complexes |b Morse homology and cohomology with local coefficients |c Augustin Banyaga ; David Hurtubise ; Peter Spaeth |
264 | 1 | |a Cham, Switzerland |b Springer |c [2024] | |
264 | 4 | |c © 2024 | |
300 | |a viii, 155 Seiten |b Illustrationen, Diagramme | ||
336 | |b txt |2 rdacontent | ||
337 | |b n |2 rdamedia | ||
338 | |b nc |2 rdacarrier | ||
490 | 1 | |a Lecture notes in mathematics |v Volume 2361 | |
520 | 3 | |a 1. Introduction -- 2. The Morse Complex with Local Coefficients -- 3. The Homology Determined by the Isomorphism Class of G -- 4. Singular and CW-Homology with Local Coefficients -- 5. Twisted Morse Cohomology and Lichnerowicz Cohomology -- 6. Applications and Computations. | |
520 | 3 | |a This book gives a detailed presentation of twisted Morse homology and cohomology on closed finite-dimensional smooth manifolds. It contains a complete proof of the Twisted Morse Homology Theorem, which says that on a closed finite-dimensional smooth manifold the homology of the Morse–Smale–Witten chain complex with coefficients in a bundle of abelian groups G is isomorphic to the singular homology of the manifold with coefficients in G. It also includes proofs of twisted Morse-theoretic versions of well-known theorems such as Eilenberg's Theorem, the Poincaré Lemma, and the de Rham Theorem. The effectiveness of twisted Morse complexes is demonstrated by computing the Lichnerowicz cohomology of surfaces, giving obstructions to spaces being associative H-spaces, and computing Novikov numbers. Suitable for a graduate level course, the book may also be used as a reference for graduate students and working mathematicians or physicists. | |
700 | 1 | |a Hurtubise, David |0 (DE-588)1012546365 |4 aut | |
700 | 1 | |a Späth, Peter |0 (DE-588)1159794553 |4 aut | |
776 | 0 | 8 | |i Erscheint auch als |a Banyaga, Augustin |t Twisted Morse Complexes |b 1st ed. 2024. |d Cham : Springer Nature Switzerland, 2024 |n Online-Ausgabe |z 978-3-031-71616-4 |
830 | 0 | |a Lecture notes in mathematics |v Volume 2361 |w (DE-604)BV000676446 |9 2361 | |
943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-035294174 |
Datensatz im Suchindex
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adam_text | |
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author | Banyaga, Augustin 1947- Hurtubise, David Späth, Peter |
author_GND | (DE-588)15213056X (DE-588)1012546365 (DE-588)1159794553 |
author_facet | Banyaga, Augustin 1947- Hurtubise, David Späth, Peter |
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author_sort | Banyaga, Augustin 1947- |
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building | Verbundindex |
bvnumber | BV049956245 |
classification_rvk | SI 850 |
ctrlnum | (OCoLC)1472072146 (DE-599)KXP1908867566 |
discipline | Mathematik |
format | Book |
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id | DE-604.BV049956245 |
illustrated | Illustrated |
indexdate | 2025-01-28T11:06:12Z |
institution | BVB |
isbn | 9783031716157 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-035294174 |
oclc_num | 1472072146 |
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owner_facet | DE-188 DE-83 |
physical | viii, 155 Seiten Illustrationen, Diagramme |
publishDate | 2024 |
publishDateSearch | 2024 |
publishDateSort | 2024 |
publisher | Springer |
record_format | marc |
series | Lecture notes in mathematics |
series2 | Lecture notes in mathematics |
spelling | Banyaga, Augustin 1947- (DE-588)15213056X aut Twisted Morse complexes Morse homology and cohomology with local coefficients Augustin Banyaga ; David Hurtubise ; Peter Spaeth Cham, Switzerland Springer [2024] © 2024 viii, 155 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics Volume 2361 1. Introduction -- 2. The Morse Complex with Local Coefficients -- 3. The Homology Determined by the Isomorphism Class of G -- 4. Singular and CW-Homology with Local Coefficients -- 5. Twisted Morse Cohomology and Lichnerowicz Cohomology -- 6. Applications and Computations. This book gives a detailed presentation of twisted Morse homology and cohomology on closed finite-dimensional smooth manifolds. It contains a complete proof of the Twisted Morse Homology Theorem, which says that on a closed finite-dimensional smooth manifold the homology of the Morse–Smale–Witten chain complex with coefficients in a bundle of abelian groups G is isomorphic to the singular homology of the manifold with coefficients in G. It also includes proofs of twisted Morse-theoretic versions of well-known theorems such as Eilenberg's Theorem, the Poincaré Lemma, and the de Rham Theorem. The effectiveness of twisted Morse complexes is demonstrated by computing the Lichnerowicz cohomology of surfaces, giving obstructions to spaces being associative H-spaces, and computing Novikov numbers. Suitable for a graduate level course, the book may also be used as a reference for graduate students and working mathematicians or physicists. Hurtubise, David (DE-588)1012546365 aut Späth, Peter (DE-588)1159794553 aut Erscheint auch als Banyaga, Augustin Twisted Morse Complexes 1st ed. 2024. Cham : Springer Nature Switzerland, 2024 Online-Ausgabe 978-3-031-71616-4 Lecture notes in mathematics Volume 2361 (DE-604)BV000676446 2361 |
spellingShingle | Banyaga, Augustin 1947- Hurtubise, David Späth, Peter Twisted Morse complexes Morse homology and cohomology with local coefficients Lecture notes in mathematics |
title | Twisted Morse complexes Morse homology and cohomology with local coefficients |
title_auth | Twisted Morse complexes Morse homology and cohomology with local coefficients |
title_exact_search | Twisted Morse complexes Morse homology and cohomology with local coefficients |
title_full | Twisted Morse complexes Morse homology and cohomology with local coefficients Augustin Banyaga ; David Hurtubise ; Peter Spaeth |
title_fullStr | Twisted Morse complexes Morse homology and cohomology with local coefficients Augustin Banyaga ; David Hurtubise ; Peter Spaeth |
title_full_unstemmed | Twisted Morse complexes Morse homology and cohomology with local coefficients Augustin Banyaga ; David Hurtubise ; Peter Spaeth |
title_short | Twisted Morse complexes |
title_sort | twisted morse complexes morse homology and cohomology with local coefficients |
title_sub | Morse homology and cohomology with local coefficients |
volume_link | (DE-604)BV000676446 |
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