算法拓?fù)鋵W(xué)及三維流形的分類

內(nèi)容概要

　　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.
　　

書籍目錄

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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