Twisted Morse Complexes
Morse Homology and Cohomology with Local Coefficients
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Beschreibung
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.
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.
Contains a complete proof of the Twisted Morse Homology Theorem Proves twisted Morse-theoretic versions of Eilenberg's Theorem, the Poincaré Lemma, and the de Rham Theorem Includes applications of twisted Morse homology to Lichnerowicz cohomology, H-spaces, and Novikov homology
Autor*in
Augustin Banyaga
Themen in »Twisted Morse Complexes«
Morse Theory Morse Homology Morse-Smale Local Coefficients CW-Complex Novikov Homology Lichnerowicz Cohomology H-Space Locally Conformal Symplectic Manifold Sheaf Cohomology
Stimmen zu »Twisted Morse Complexes«
“This book gives a detailed presentation of twisted Morse homology and Morse cohomology on closed, finite-dimensional, smooth Riemannian manifolds. … The very delicate material treated in the book is carefully explained, and there are excellent descriptions of Morse theoretical notions and homology theory with local coefficients. The book is on an advanced level and has the character of a research monograph. As such, it is a valuable and well-written contribution to algebraic and differential topology of manifolds.” (Vagn Lundsgaard Hansen, Mathematical Reviews, February, 2026)
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