Beschreibung
From the reviews of the 1st edition: "This book provides a comprehensive and detailed account of different topics in algorithmic 3-dimensional topology, culminating with the recognition procedure for Haken manifolds and including the up-to-date results in computer enumeration of 3-manifolds. Originating from lecture notes of various courses given by the author over a decade, the book is intended to combine the pedagogical approach of a graduate textbook (without exercises) with the completeness and reliability of a research monograph All the material, with few exceptions, is presented from the peculiar point of view of special polyhedra and special spines of 3-manifolds. This choice contributes to keep the level of the exposition really elementary. In conclusion, the reviewer subscribes to the quotation from the back cover: "the book fills a gap in the existing literature and will become a standard reference for algorithmic 3-dimensional topology both for graduate students and researchers". Zentralblatt für Mathematik 2004 For this 2nd edition, new results, new proofs, and commentaries for a better orientation of the reader have been added. In particular, in Chapter 7 several new sections concerning applications of the computer program "3-Manifold Recognizer" have been included.
Inhaltsverzeichnis
1 Simple and Special Polyhedra.- 2 Complexity Theory of 3-Manifolds.- 3 Haken Theory of Normal Surfaces.- 4 Applications of the Theory of Normal Surfaces.- 5 Algorithmic Recognition of $S^3$.- 6 Classification of Haken 3-Manifolds.- 7 3-Manifold Recognizer.- 8 The Turaev-Viro Invariants.- Appendix.- 9.1 Manifolds of Complexity $\leq 6.- 9.2 Minimal Spines of Manifolds up to Complexity 6.- 9.3 Minimal Spines of Some Manifolds of Complexity 7.- 9.4 Tables of Turaev-Viro Invariants.- References.- Index
Autorenporträt
InhaltsangabeSimple and Special Polyhedra.- Complexity Theory of 3-Manifolds.- Haken Theory of Normal Surfaces.- Applications of the Theory of Normal Surfaces.- Algorithmic Recognition of S3.- Classification of Haken 3-Manifolds.- 3-Manifold Recognizer.- The Turaev-Viro Invariants.
Herstellerkennzeichnung:
Springer Verlag GmbH
Tiergartenstr. 17
69121 Heidelberg
DE
E-Mail: juergen.hartmann@springer.com
