Topology for Computing [Hardcover]

This book presents basic concepts from the emerging field of computational topology, now being used to solve problems in diverse fields.Written by a computer scientist for computer scientists, this book teaches topology from a computational point of view, seeking to solve real problems that have topological aspects using computers. Such problems arise in many areas, such as computer graphics, robotics, structural biology, and chemistry. The author starts from the basics of topology, assuming no prior exposure to the subject, and moves rapidly up to recent advances in the area, including topological persistence and hierarchical Morse complexes, presenting algorithms and data structures when appropriate.Written by a computer scientist for computer scientists, this book teaches topology from a computational point of view, seeking to solve real problems that have topological aspects using computers. Such problems arise in many areas, such as computer graphics, robotics, structural biology, and chemistry. The author starts from the basics of topology, assuming no prior exposure to the subject, and moves rapidly up to recent advances in the area, including topological persistence and hierarchical Morse complexes, presenting algorithms and data structures when appropriate.Written by a computer scientist for computer scientists, this book teaches topology from a computational point of view, and shows how to solve real problems that have topological aspects involving computers. Such problems arise in many areas, such as computer graphics, robotics, structural biology, and chemistry. The author starts from the basics of topology, assuming no prior exposure to the subject, and moves rapidly up to recent advances in the area, including topological persistence and hierarchical Morse complexes. Algorithms and data structures are presented when appropriate.1. Introduction; Part I. Mathematics: 2. Spaces and filtrations; 3. Group theory; 4. Homology; 5. Morse theory; 6. New resull³³