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.
General
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