Lecture Notes in Mathematics: Morse Homology and Cohomology with Local Coefficients

Banyaga, Augustin; Hurtubise, David; Spaeth, Peter

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.

Details

Published by: Springer

Publication Date: 2024-11-02

Format: Paperback

ISBN-13: 9783031716157

DOI: 10.1007/978-3-031-71616-4

Dimensions: 235cm x155cm

Pages: 158