LEADER 03449nam 22006495 450 001 9910903799103321 005 20260126114824.0 010 $a3-031-71616-7 024 7 $a10.1007/978-3-031-71616-4 035 $a(CKB)36527925800041 035 $a(PPN)281830444 035 $a(DE-He213)978-3-031-71616-4 035 $a(EXLCZ)9936527925800041 100 $a20241102d2024 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aTwisted Morse Complexes $eMorse Homology and Cohomology with Local Coefficients /$fby Augustin Banyaga, David Hurtubise, Peter Spaeth 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (VIII, 158 p. 58 illus.) 225 1 $aLecture Notes in Mathematics,$x1617-9692 ;$v2361 311 08$a3-031-71615-9 327 $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. 330 $aThis book gives a detailed presentation of twisted Morse homology and cohomology on closed finite-dimensional smooth manifolds. It contains a complete proof of the Twisted Morse Homology Theorem, which says that on a closed finite-dimensional smooth manifold the homology of the Morse?Smale?Witten chain complex with coefficients in a bundle of abelian groups G is isomorphic to the singular homology of the manifold with coefficients in G. It also includes proofs of twisted Morse-theoretic versions of well-known theorems such as Eilenberg's Theorem, the Poincaré Lemma, and the de Rham Theorem. The effectiveness of twisted Morse complexes is demonstrated by computing the Lichnerowicz cohomology of surfaces, giving obstructions to spaces being associative H-spaces, and computing Novikov numbers. Suitable for a graduate level course, the book may also be used as a reference for graduate students and working mathematicians or physicists. 410 0$aLecture Notes in Mathematics,$x1617-9692 ;$v2361 606 $aDynamics 606 $aAlgebraic topology 606 $aManifolds (Mathematics) 606 $aGlobal analysis (Mathematics) 606 $aDynamical Systems 606 $aAlgebraic Topology 606 $aManifolds and Cell Complexes 606 $aGlobal Analysis and Analysis on Manifolds 606 $aHomologia$2thub 606 $aTeoria de Morse$2thub 608 $aLlibres electrònics$2thub 615 0$aDynamics. 615 0$aAlgebraic topology. 615 0$aManifolds (Mathematics) 615 0$aGlobal analysis (Mathematics) 615 14$aDynamical Systems. 615 24$aAlgebraic Topology. 615 24$aManifolds and Cell Complexes. 615 24$aGlobal Analysis and Analysis on Manifolds. 615 7$aHomologia 615 7$aTeoria de Morse 676 $a515.39 700 $aBanyaga$b Augustin$4aut$4http://id.loc.gov/vocabulary/relators/aut$0622064 702 $aHurtubise$b David$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aSpaeth$b Peter$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910903799103321 996 $aTwisted Morse Complexes$94436050 997 $aUNINA