國立虎尾科技大學 |

Twisted Morse complexes = Morse homology and cohomology with local coefficients /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Twisted Morse complexes/ by Augustin Banyaga, David Hurtubise, Peter Spaeth.
其他題名:	Morse homology and cohomology with local coefficients /
作者:	Banyaga, Augustin.
其他作者:	Spaeth, Peter.
出版者:	Cham :Springer Nature Switzerland : : 2024.,
面頁冊數:	viii, 158 p. :ill., digital ; : 24 cm.;
Contained By:	Springer Nature eBook
標題:	Global Analysis and Analysis on Manifolds. -
電子資源:	https://doi.org/10.1007/978-3-031-71616-4
ISBN:	9783031716164

Twisted Morse complexes = Morse homology and cohomology with local coefficients /
Banyaga, Augustin.

Twisted Morse complexesMorse homology and cohomology with local coefficients /[electronic resource] :by Augustin Banyaga, David Hurtubise, Peter Spaeth. - Cham :Springer Nature Switzerland :2024. - viii, 158 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v. 23611617-9692 ;. - Lecture notes in mathematics ;1943..

- 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.

ISBN: 9783031716164

Standard No.: 10.1007/978-3-031-71616-4doiSubjects--Topical Terms:

672519
Global Analysis and Analysis on Manifolds.

LC Class. No.: QA612.3

Dewey Class. No.: 514.23

Twisted Morse complexes = Morse homology and cohomology with local coefficients /
LDR:02324nam a2200337 a 4500 001 1138472
003 DE-He213
005 20241102115734.0
006 m d
007 cr nn 008maaau
008 250117s2024 sz s 0 eng d
020 $a 9783031716164 $q (electronic bk.)
020 $a 9783031716157 $q (paper)
024 7 $a 10.1007/978-3-031-71616-4 $2 doi
035 $a 978-3-031-71616-4
040 $a GP $c GP
041 0 $a eng
050 4 $a QA612.3
072 7 $a GPFC $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a GPFC $2 thema
082 0 4 $a 514.23 $2 23
090 $a QA612.3 $b .B219 2024
100 1 $a Banyaga, Augustin. $3 1132459
245 1 0 $a Twisted Morse complexes $h [electronic resource] : $b Morse homology and cohomology with local coefficients / $c by Augustin Banyaga, David Hurtubise, Peter Spaeth.
260 $a Cham : $c 2024. $b Springer Nature Switzerland : $b Imprint: Springer,
300 $a viii, 158 p. : $b ill., digital ; $c 24 cm.
490 1 $a Lecture notes in mathematics, $x 1617-9692 ; $v v. 2361
505 0 $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 $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.
650 2 4 $a Global Analysis and Analysis on Manifolds. $3 672519
650 2 4 $a Manifolds and Cell Complexes. $3 1366170
650 2 4 $a Algebraic Topology. $3 672209
650 1 4 $a Dynamical Systems. $3 1366074
650 0 $a Homology theory. $3 682984
650 0 $a Morse theory. $3 678127
700 1 $a Spaeth, Peter. $3 1462204
700 1 $a Hurtubise, David. $3 1462203
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
830 0 $a Lecture notes in mathematics ; $v 1943. $3 882220
856 4 0 $u https://doi.org/10.1007/978-3-031-71616-4
950 $a Mathematics and Statistics (SpringerNature-11649)