03449nam 22006495 450 991090379910332120260126114824.03-031-71616-710.1007/978-3-031-71616-4(CKB)36527925800041(PPN)281830444(DE-He213)978-3-031-71616-4(EXLCZ)993652792580004120241102d2024 u| 0engur|||||||||||txtrdacontentcrdamediacrrdacarrierTwisted Morse Complexes Morse Homology and Cohomology with Local Coefficients /by Augustin Banyaga, David Hurtubise, Peter Spaeth1st ed. 2024.Cham :Springer Nature Switzerland :Imprint: Springer,2024.1 online resource (VIII, 158 p. 58 illus.)Lecture Notes in Mathematics,1617-9692 ;23613-031-71615-9 - 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.Lecture Notes in Mathematics,1617-9692 ;2361DynamicsAlgebraic topologyManifolds (Mathematics)Global analysis (Mathematics)Dynamical SystemsAlgebraic TopologyManifolds and Cell ComplexesGlobal Analysis and Analysis on ManifoldsHomologiathubTeoria de MorsethubLlibres electrònicsthubDynamics.Algebraic topology.Manifolds (Mathematics)Global analysis (Mathematics)Dynamical Systems.Algebraic Topology.Manifolds and Cell Complexes.Global Analysis and Analysis on Manifolds.HomologiaTeoria de Morse515.39Banyaga Augustinauthttp://id.loc.gov/vocabulary/relators/aut622064Hurtubise Davidauthttp://id.loc.gov/vocabulary/relators/autSpaeth Peterauthttp://id.loc.gov/vocabulary/relators/autBOOK9910903799103321Twisted Morse Complexes4436050UNINA