Twisted Morse Complexes : Morse Homology and Cohomology with Local Coefficients / by Augustin Banyaga, David Hurtubise, Peter Spaeth.

Format:

Book

Author/Creator:

Banyaga, Augustin, Author.

Hurtubise, David, Author.

Spaeth, Peter, Author.

Series:

Lecture Notes in Mathematics, 1617-9692 ; 2361

Language:

English

Subjects (All):

Dynamics.

Algebraic topology.

Manifolds (Mathematics).

Global analysis (Mathematics).

Dynamical Systems.

Algebraic Topology.

Manifolds and Cell Complexes.

Global Analysis and Analysis on Manifolds.

Local Subjects:

Dynamical Systems.

Algebraic Topology.

Manifolds and Cell Complexes.

Global Analysis and Analysis on Manifolds.

Physical Description:

1 online resource (VIII, 158 p. 58 illus.)

Edition:

1st ed. 2024.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Springer, 2024.

Summary:

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.

Contents:

- 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.

ISBN:

3-031-71616-7