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.
My goal in this book is to enable a non-specialist to grasp and participate
in current research in computational topology. Therefore, this book is not a
compilation of recent advances in the area. Rather, the book presents basic
mathematical concepts from a computer scientist’s point of view, focusing on
computational challenges and introducing algorithms and data structures when
appropriate. The book also incorporates several recent results from my doctoral
dissertation and subsequent related results in computational topology.
The primary motivation for this book is the significance and utility of topological
concepts in solving problems in computer science. These problems
arise naturally in computational geometry, graphics, robotics, structural biology,
and chemistry. Often, the questions themselves have been known and
considered by topologists.