**Student Mathematical Library**

Volume: 90;
2019;
273 pp;
Softcover

MSC: Primary 55; 58; 57;

**Print ISBN: 978-1-4704-5298-8
Product Code: STML/90**

List Price: $55.00

AMS Member Price: $44.00

MAA Member Price: $44.00

**Electronic ISBN: 978-1-4704-5379-4
Product Code: STML/90.E**

List Price: $55.00

AMS Member Price: $44.00

MAA Member Price: $44.00

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#### Supplemental Materials

# Discrete Morse Theory

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*Nicholas A. Scoville*

Discrete Morse theory is a powerful tool combining ideas in both
topology and combinatorics. Invented by Robin Forman in the mid 1990s,
discrete Morse theory is a combinatorial analogue of Marston Morse's
classical Morse theory. Its applications are vast, including
applications to topological data analysis, combinatorics, and computer
science.

This book, the first one devoted solely to discrete Morse
theory, serves as an introduction to the subject. Since the book
restricts the study of discrete Morse theory to abstract simplicial
complexes, a course in mathematical proof writing is the only
prerequisite needed. Topics covered include simplicial complexes,
simple homotopy, collapsibility, gradient vector fields, Hasse
diagrams, simplicial homology, persistent homology, discrete Morse
inequalities, the Morse complex, discrete Morse homology, and strong
discrete Morse functions. Students of computer science will also find
the book beneficial as it includes topics such as Boolean functions,
evasiveness, and has a chapter devoted to some computational aspects
of discrete Morse theory. The book is appropriate for a course in
discrete Morse theory, a supplemental text to a course in algebraic
topology or topological combinatorics, or an independent study.

An instructor's manual for this title is available electronically
to those instructors who have already adopted the textbook for classroom use.
Please send email to textbooks@ams.org for more
information.

#### Readership

Undergraduate and graduate students interested in discrete Morse theory.

#### Table of Contents

# Table of Contents

## Discrete Morse Theory

- Cover Cover11
- Title page i2
- Preface ix10
- Chapter 0. What is discrete Morse theory? 116
- Chapter 1. Simplicial complexes 1530
- Chapter 2. Discrete Morse theory 4156
- Chapter 3. Simplicial homology 8196
- Chapter 4. Main theorems of discrete Morse theory 101116
- Chapter 5. Discrete Morse theory and persistent homology 117132
- Chapter 6. Boolean functions and evasiveness 149164
- Chapter 7. The Morse complex 169184
- Chapter 8. Morse homology 187202
- Chapter 9. Computations with discrete Morse theory 209224
- Chapter 10. Strong discrete Morse theory 233248
- Bibliography 257272
- Notation and symbol index 265280
- Index 267282
- Back cover Back cover1289