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020 _a9783031716164
_9978-3-031-71616-4
024 7 _a10.1007/978-3-031-71616-4
_2doi
050 4 _aQA843-871
072 7 _aGPFC
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aGPFC
_2thema
100 1 _aBanyaga, Augustin.
_eauthor.
_0(orcid)0000-0003-2436-5496
_1https://orcid.org/0000-0003-2436-5496
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_986979
245 1 0 _aTwisted Morse Complexes
_h[electronic resource] :
_bMorse Homology and Cohomology with Local Coefficients /
_cby Augustin Banyaga, David Hurtubise, Peter Spaeth.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aVIII, 158 p. 58 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x1617-9692 ;
_v2361
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 _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.
650 0 _aDynamical systems.
650 0 _aAlgebraic topology.
650 0 _aManifolds (Mathematics).
_969683
650 0 _aGlobal analysis (Mathematics).
_969682
650 1 4 _aDynamical Systems.
650 2 4 _aAlgebraic Topology.
650 2 4 _aManifolds and Cell Complexes.
_973090
650 2 4 _aGlobal Analysis and Analysis on Manifolds.
_969685
700 1 _aHurtubise, David.
_eauthor.
_0(orcid)0000-0003-4255-4776
_1https://orcid.org/0000-0003-4255-4776
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_986980
700 1 _aSpaeth, Peter.
_eauthor.
_0(orcid)0000-0001-7674-4717
_1https://orcid.org/0000-0001-7674-4717
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_986981
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031716157
776 0 8 _iPrinted edition:
_z9783031716171
830 0 _aLecture Notes in Mathematics,
_x1617-9692 ;
_v2361
_975434
856 4 0 _uhttps://doi.org/10.1007/978-3-031-71616-4
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
912 _aZDB-2-LNM
999 _c64692
_d64692