算法拓撲學及三維流形的分類

算法拓撲學及三維流形的分類

taries orien tation

作 者:(俄)馬特維耶夫 編著
出 版 社:科學出版社
出版時間:2011-6-1
頁 數:492
字 數:630000
印刷時間:2011-6-1
開 本:16開

內容簡介

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".R. Piergallini, Zentralblattfilr Mathematik 1048 (2004) For this 2nd edition, new results, new proofs, and commentaries for a better orientation of the reader have been added.

目錄

1 simple and special polyhedra
1.1 spines of 3-manifolds
1.2 elementary moves on special spines
1.3 special polyhedra which are not spines
2 complexity theory of 3-manifolds
2.1what is the complexity of a 3-manifold?
2.2properties of complexity
2.3closed manifolds of small complexity
2.4graph manifolds of waldhausen
2.5hyperbolic manifolds
2.6lower bounds of the complexity
3 haken theory of normal surfaces
3.1 basic notions and haken's scheme
3.2 theory of normal curves
3.3 normal surfaces in 3-manifolds
3.4 normal surfaces in handle decompositions
4 applications of the theory of normal surfaces
6 Classification of Haken 3-Manifolds
5 algorithmic recognition of sa
7 3-manifold recognizer
8 the turaev-viro invariants
references
index

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