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xiii, 243 p. : ill. (some col.) ; 24 cm.
  • 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.
  • (source: Nielsen Book Data)9780521836661 20160528
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.
(source: Nielsen Book Data)9780521836661 20160528
Science Library (Li and Ma)
xiv, 450 p. : ill.
  • Part 1 Basic theory: E-graphs - special cell-decomposition of 2-manifolds-- crystallizations - the Ferri-Gagliardi moves-- diagrams of E-graphs and Ferri's switching lemma. Part 2 Generating surgery moves: quadricolours, hinges, commuters-- relations among the generating moves-- connections with Lickorish's construction. Part 3 Invariants: the fundamental and the homology groups-- the vertex group ... is there something new here?-- linking invariants. Part 4 Classes of 3-gems: the "planar" class and lens spaces-- gists - special symmetries on 3-manifolds. Part 5 Theory for a catalogue of 3-gems: shortcuts for inserting the 4th colour-- the TS-moves and the U-move. Appendices: all 3-gems up to 28 vertices. (Part Contents).
  • (source: Nielsen Book Data)9789810219079 20160614
This text provides a guide to dealing with 3-manifolds by computers. Its emphasis is on presenting algorithms which are used for solving (in practice) the homeomorphism problem for the smallest of these objects. The key concept is the 3-gem, a special kind of edge-colored graph, which encodes the manifold via a ball complex. Passages between 3-gems and more standard presentations like Heegaard diagrams and surgery descriptions are provided. A catalogue of all closed orientable 3-manifolds induced by 3-gems up to 30 vertices is included. In order to help the classification, various invariants are presented, including the new quantum invariants.
(source: Nielsen Book Data)9789810219079 20160614
xii, 241 p. : ill. ; 27 cm.
Combining concepts from topology and algorithms, this book delivers what its title promises: an introduction to the field of computational topology. Starting with motivating problems in both mathematics and computer science and building up from classic topics in geometric and algebraic topology, the third part of the text advances to persistent homology. This point of view is critically important in turning a mostly theoretical field of mathematics into one that is relevant to a multitude of disciplines in the sciences and engineering. The main approach is the discovery of topology through algorithms. The book is ideal for teaching a graduate or advanced undergraduate course in computational topology, as it develops all the background of both the mathematical and algorithmic aspects of the subject from first principles. Thus the text could serve equally well in a course taught in a mathematics department or computer science department.
(source: Nielsen Book Data)9780821849255 20160604
Science Library (Li and Ma)
viii, 317 p. : ill. ; 25 cm.
SAL3 (off-campus storage)


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