Algorithmic Topology and Classification of 3-Manifolds

2. Auflage 2007
ISBN: 978-3-642-07960-3
Verlag: Springer

Buch, Englisch, 492 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 762 g

Reihe: Algorithms and Computation in Mathematics

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 2 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.

Zielgruppe

Graduate

Autoren/Hrsg.

Matveev, Sergei

Fachgebiete

• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen
• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Algorithmen & Datenstrukturen

Inhaltsverzeichnis

Simple 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.