Description
Book SynopsisMorse Theory: Smooth and Discrete serves as an introduction to classical smooth Morse theory and to Forman's discrete Morse theory, highlighting the parallels between the two subjects. This is the first time both smooth and discrete Morse theory have been treated in a single volume. This makes the book a valuable resource for students and professionals working in topology and discrete mathematics. With a strong focus on examples, the text is suitable for advanced undergraduates or beginning graduate students.
Table of ContentsSmooth Morse Theory: First Steps (Surfaces, Critical Points); Fundamental Results (Morse Lemma, Existence, Gradient-Like Vector Fields); Topological Consequences (Homotopy Type, Morse Inequalities); Discrete Morse Theory: First Steps (Definitions and Examples); Fundamental Results (Existence, Gradients); Topological Consequences (Homotopy Type, Collapses); Algorithms (Constructing Discrete Morse Functions); Appendices: Smooth Manifolds; Simplicial Complexes;
