03717nam a22005895i 4500 978-3-031-71616-4 DE-He213 20251030113257.0 cr nn 008mamaa 241102s2024 sz | s |||| 0|eng d 9783031716164 978-3-031-71616-4 10.1007/978-3-031-71616-4 doi QA843-871 GPFC bicssc MAT034000 bisacsh GPFC thema Banyaga, Augustin. author. (orcid)0000-0003-2436-5496 https://orcid.org/0000-0003-2436-5496 aut http://id.loc.gov/vocabulary/relators/aut 86979 Twisted Morse Complexes [electronic resource] : Morse Homology and Cohomology with Local Coefficients / by Augustin Banyaga, David Hurtubise, Peter Spaeth. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. VIII, 158 p. 58 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Lecture Notes in Mathematics, 1617-9692 ; 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. Dynamical systems. Algebraic topology. Manifolds (Mathematics). 69683 Global analysis (Mathematics). 69682 Dynamical Systems. Algebraic Topology. Manifolds and Cell Complexes. 73090 Global Analysis and Analysis on Manifolds. 69685 Hurtubise, David. author. (orcid)0000-0003-4255-4776 https://orcid.org/0000-0003-4255-4776 aut http://id.loc.gov/vocabulary/relators/aut 86980 Spaeth, Peter. author. (orcid)0000-0001-7674-4717 https://orcid.org/0000-0001-7674-4717 aut http://id.loc.gov/vocabulary/relators/aut 86981 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031716157 Printed edition: 9783031716171 Lecture Notes in Mathematics, 1617-9692 ; 2361 75434 https://doi.org/10.1007/978-3-031-71616-4 ZDB-2-SMA ZDB-2-SXMS ZDB-2-LNM 64692 64692