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Twisted Morse complexesMorse homology and cohomology with local coefficients /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Twisted Morse complexesby Augustin Banyaga, David Hurtubise, Peter Spaeth.
Reminder of title:	Morse homology and cohomology with local coefficients /
Author:	Banyaga, Augustin.
other author:	Hurtubise, David.
Published:	Cham :Springer Nature Switzerland :2024.
Description:	viii, 158 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Morse theory.
Online resource:	https://doi.org/10.1007/978-3-031-71616-4
ISBN:	9783031716164$q(electronic bk.)

Twisted Morse complexesMorse 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 ;2035..

- 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$q(electronic bk.)

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

275672
Morse theory.

LC Class. No.: QA612.3

Dewey Class. No.: 514.23

Twisted Morse complexesMorse homology and cohomology with local coefficients /
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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 0 $a Morse theory. $3 275672
650 0 $a Homology theory. $3 205880
650 1 4 $a Dynamical Systems. $3 913342
650 2 4 $a Algebraic Topology. $3 273784
650 2 4 $a Manifolds and Cell Complexes. $3 913127
650 2 4 $a Global Analysis and Analysis on Manifolds. $3 273786
700 1 $a Hurtubise, David. $3 984452
700 1 $a Spaeth, Peter. $3 984453
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