算法拓扑学及三维流形的分类 （第二版 英文影印版） 作 者： （俄）马特维耶夫 编著 出版时间：2011 内容简介 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 录 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
