Lectures on Morse Homology (Texts in the Mathematical Sciences)
Edition: 1 edition
Publisher: Springer
Published: October 13, 2005
Language: eng
Format: Hardcover
Number of pages: 326
ISBN-13: 9781402026959
Subjects: Algebraic topology; Science; Mathematical Analysis; Mathematics; Science/Mathematics; Differential Equations; Group Theory; Homology theory; Mathematics / Mathematical Analysis; Mathematics : Differential Equations; Mathematics : Group Theory; Morse theory; Research & Methodology
First sentence: A Morse-Smale function f : M R on a finite dimensional compact smooth Riemannian manifold (M, g) gives rise to a chain complex (C*(f), *), called the Morse-Smale-Witten chain complex (Definition 7.2), whose chains are generated by the critical points of f and whose boundary operator is defined by counting gradient flow lines (with sign).