Algorithmic Topology And Classification Of 3 Manifolds
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Algorithmic Topology and Classification of 3-Manifolds
Author: Sergei Matveev
language: en
Publisher: Springer Science & Business Media
Release Date: 2007-08-13
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.
Algorithmic Topology and Classification of 3-Manifolds
Author: Sergei Matveev
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-04-17
The book is devoted to algorithmic low-dimensional topology. This branch of mathematics has recently been undergoing an intense development. On the one hand, the exponential advancement of computer technologies has made it possible to conduct sophisticated computer experiments and to implement algorithmic solutions, which have in turn provided a motivation to search for new and better algorithms. On the other hand, low-dimensional topology has received an additional boost because of the discovery of numerous connections with theoretical physics. There is also another deep reason why algorithmic topology has received a lot of attention. It is that a search for algorithmic solutions generally proves to be a rich source of well-stated mathematical problems. Speaking out of my experience, it seems that an orientation towards "how to" rather than just "how is" serves as a probing stone for choosing among possible directions of research - much like problems in mechanics led once to the development of calculus.
Algorithmic Topology and Classification of 3-Manifolds
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.