Afra J. Zomorodian

Topology for Computing (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

---

Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.

Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 10. Januar 2005
• Englisch
• ISBN-13: 9780511081309
• Artikelnr.: 38188853

Autorenporträt

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, California and has been a researcher at the Max-Planck-Institut für Informatik, Saarbrücken. Using the material contained in this book, he has organized classes on computational topology at Stanford University, the MPI, and Dartmouth College.

Inhaltsangabe

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.