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

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Twisted Morse complexes/ by 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

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:

678127
Morse theory.

LC Class. No.: QA612.3

Dewey Class. No.: 514.23

Twisted Morse complexes = Morse homology and cohomology with local coefficients /
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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.
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650 2 4 $a Manifolds and Cell Complexes. $3 1366170
650 2 4 $a Global Analysis and Analysis on Manifolds. $3 672519
700 1 $a Hurtubise, David. $3 1462203
700 1 $a Spaeth, Peter. $3 1462204
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