算法拓扑学及三维流形的分类-(第二版)-教辅教材-文化科教-太极之巅书单号

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算法拓扑学及三维流形的分类-(第二版) 内容简介

from the reviews of the 1st edition: "thisbook provides a comprehensive and detailed account of differenttopics in algorithmic 3-dimensional topology, culminating with therecognition procedure for haken manifolds and including theup-to-date results in computer enumeration of 3-manifolds.originating from lecture notes of various courses given by theauthor over a decade, the book is intended to combine thepedagogical 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 thepeculiar point of view of special polyhedra and special spines of3-manifolds. this choice contributes to keep the level of theexposition really elementary. in conclusion, the reviewersubscribes to the quotation from the back cover: "the book fills agap in the existing literature and will become a standard referencefor algorithmic 3-dimensional topology both for graduate studentsand researchers".r. piergallini, zentralblattfilr mathematik 1048(2004) for this 2nd edition, new results, new proofs, andcommentaries for a better orientation of the reader have beenadded.

算法拓扑学及三维流形的分类-(第二版) 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