Cover 1
Title page 2
Preface 10
Chapter 0. What is discrete Morse theory? 16
0.1. What is discrete topology? 17
0.2. What is Morse theory? 24
0.3. Simplifying with discrete Morse theory 28
Chapter 1. Simplicial complexes 30
1.1. Basics of simplicial complexes 30
1.2. Simple homotopy 46
Chapter 2. Discrete Morse theory 56
2.1. Discrete Morse functions 59
2.2. Gradient vector fields 71
2.3. Random discrete Morse theory 88
Chapter 3. Simplicial homology 96
3.1. Linear algebra 97
3.2. Betti numbers 101
3.3. Invariance under collapses 110
Chapter 4. Main theorems of discrete Morse theory 116
4.1. Discrete Morse inequalities 116
4.2. The collapse theorem 126
Chapter 5. Discrete Morse theory and persistent homology 132
5.1. Persistence with discrete Morse functions 132
5.2. Persistent homology of discrete Morse functions 149
Chapter 6. Boolean functions and evasiveness 164
6.1. A Boolean function game 164
6.2. Simplicial complexes are Boolean functions 167
6.3. Quantifying evasiveness 170
6.4. Discrete Morse theory and evasiveness 173
Chapter 7. The Morse complex 184
7.1. Two definitions 184
7.2. Rooted forests 192
7.3. The pure Morse complex 194
Chapter 8. Morse homology 202
8.1. Gradient vector fields revisited 203
8.2. The flow complex 210
8.3. Equality of homology 211
8.4. Explicit formula for homology 214
8.5. Computation of Betti numbers 220
Chapter 9. Computations with discrete Morse theory 224
9.1. Discrete Morse functions from point data 224
9.2. Iterated critical complexes 235
Chapter 10. Strong discrete Morse theory 248
10.1. Strong homotopy 248
10.2. Strong discrete Morse theory 257
10.3. Simplicial Lusternik-Schnirelmann category 264
Bibliography 272
Notation and symbol index 280
Index 282
Back cover 289
Preface
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Table of Contents
Index
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还没人写过短评呢
还没人写过短评呢