TY  - BOOK
AU  - Banyaga,Augustin
AU  - Hurtubise,David
AU  - Spaeth,Peter
ED  - SpringerLink (Online service)
TI  - Twisted Morse Complexes: Morse Homology and Cohomology with Local Coefficients 
T2  - Lecture Notes in Mathematics,
SN  - 9783031716164
AV  - QA843-871 
PY  - 2024///
CY  - Cham
PB  - Springer Nature Switzerland, Imprint: Springer
KW  - Dynamical systems
KW  - Algebraic topology
KW  - Manifolds (Mathematics)
KW  - Global analysis (Mathematics)
KW  - Dynamical Systems
KW  - Algebraic Topology
KW  - Manifolds and Cell Complexes
KW  - Global Analysis and Analysis on Manifolds
N1  - - 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
N2  - 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
UR  - https://doi.org/10.1007/978-3-031-71616-4
ER  -