Topology for Computing

Erscheinungsjahr 2016
ISBN: 978-0-521-13609-9
Verlag: Cambridge University Press

Buch, Englisch, Band 16, 258 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 427 g

Reihe: Cambridge Monographs on Applied and Computational Mathematics

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.

Autoren/Hrsg.

Zomorodian, Afra J.

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker

Inhaltsverzeichnis

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.

Über Autor(innen)

Zomorodian, Afra J.
Afra J. Zomorodian is an assistant professor in the Department of Computer Science at Dartmouth College. He is a former Post-Doctoral Fellow in Bio-X and the Department of Computer Science at Stanford University and has been a researcher at the Max-Planck-Institut für Informatik in Saarbrücken, Germany. Using the material contained in this book, he has organized classes on computational topology at Stanford University, the MPI, and Dartmouth College.