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The emerging field of computational topology utilizes theory from topology and the power of computing to solve problems in diverse fields. Recent applications include computer graphics, computer-aided design (CAD), and structural biology, all of which involve understanding the intrinsic shape of some real or abstract space. A primary goal of this book is to present basic concepts from topology and Morse theory to enable a non-specialist to grasp and participate in current research in computational topology. The author gives a self-contained presentation of the mathematical concepts from a computer scientist's point of view, combining point set topology, algebraic topology, group theory, differential manifolds, and Morse theory. He also presents some recent advances in the area, including topological persistence and hierarchical Morse complexes. Throughout, the focus is on computational challenges and on presenting algorithms and data structures when appropriate.

1. Introduction

Part I. Mathematics:

　2. Spaces and filtrations

　3. Group theory

　4. Homology

　5. Morse theory

　6. New results

Part II. Algorithms:

　7. The persistence algorithms

　8. Topological simplification

　9. The Morse-Smale algorithm

　10. The linking number algorithm

Part III. Applications:

　11. Software

　12. Experiments

　13. Applications.

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编辑推荐

　　The emerging field of computational topology utilizes theory

from topology and the power of computing to solve problems in

diverse fields. Recent applications include computer graphics,

computer-aided design (CAD), and structural biology, all of which

involve understanding the intrinsic shape of some real or abstract

space. A primary goal of this book is to present basic concepts

from topology and Morse theory to enable a non-specialist to grasp

and participate in current research in computational topology. The

author gives a self-contained presentation of the mathematical

concepts from a computer scientist's point of view, combining point

set topology, algebraic topology, group theory, differential

manifolds, and Morse theory. He also presents some recent advances

in the area, including topological persistence and hierarchical

Morse complexes. Throughout, the focus is on computational

challenges and on presenting algorithms and data structures when

appropriate.

　　? Presents classical topological subject of Morse theory in a

computer science context ? Material is widely used within

computation geometry and computer graphics

书籍介绍

The emerging field of computational topology utilizes theory from topology and the power of computing to solve problems in diverse fields. Recent applications include computer graphics, computer-aided design (CAD), and structural biology, all of which involve understanding the intrinsic shape of some real or abstract space. A primary goal of this book is to present basic concepts from topology and Morse theory to enable a non-specialist to grasp and participate in current research in computational topology. The author gives a self-contained presentation of the mathematical concepts from a computer scientist's point of view, combining point set topology, algebraic topology, group theory, differential manifolds, and Morse theory. He also presents some recent advances in the area, including topological persistence and hierarchical Morse complexes. Throughout, the focus is on computational challenges and on presenting algorithms and data structures when appropriate.