Sergei Matveev's Algorithmic Topology and Classification of 3-Manifolds PDF

By Sergei Matveev

ISBN-10: 3662051028

ISBN-13: 9783662051023

ISBN-10: 3662051044

ISBN-13: 9783662051047

From the experiences of the first edition:

"This booklet offers a entire and exact account of alternative issues in algorithmic three-dimensional topology, culminating with the popularity approach for Haken manifolds and together with the updated leads to desktop enumeration of 3-manifolds. Originating from lecture notes of assorted classes given via the writer over a decade, the publication is meant to mix the pedagogical method of a graduate textbook (without workouts) with the completeness and reliability of a examine monograph…

All the fabric, with few exceptions, is gifted from the extraordinary standpoint of specific polyhedra and precise spines of 3-manifolds. This selection contributes to maintain the extent of the exposition particularly uncomplicated.

In end, the reviewer subscribes to the citation from the again conceal: "the booklet fills a spot within the present literature and may develop into a regular reference for algorithmic three-d topology either for graduate scholars and researchers".

Zentralblatt für Mathematik 2004

For this 2nd variation, new effects, new proofs, and commentaries for a greater orientation of the reader were further. specifically, in bankruptcy 7 numerous new sections relating functions of the pc software "3-Manifold Recognizer" were integrated.

Show description

Read Online or Download Algorithmic Topology and Classification of 3-Manifolds PDF

Similar differential geometry books

An Introduction to Noncommutative Geometry by Joseph C. Varilly PDF

Noncommutative geometry, encouraged through quantum physics, describes singular areas via their noncommutative coordinate algebras and metric constructions by means of Dirac-like operators. Such metric geometries are defined mathematically via Connes' idea of spectral triples. those lectures, brought at an EMS summer season university on noncommutative geometry and its purposes, supply an outline of spectral triples in line with examples.

Download e-book for kindle: Torus Actions on Symplectic Manifolds by Michèle Audin

This can be a longer moment version of "The Topology of Torus activities on Symplectic Manifolds" released during this sequence in 1991. the fabric and references were up-to-date. Symplectic manifolds and torus activities are investigated, with a variety of examples of torus activities, for example on a few moduli areas.

Additional resources for Algorithmic Topology and Classification of 3-Manifolds

Sample text

Taking a contractible polyhedron X and assuming ZC, we have X~X x I~{ *}. 35. 34 remains true if we restrict ZC to the class of special polyhedra. Only minor modifications in the proof are needed. For proving ZC :::} PC one should take not an arbitrary but a special spine X of M, and for proving ZC :::} AC one should first 3-deform X to a special polyhedron and only then take the product with I. We may conclude that (1) ZC for special spines implies PC; (2) ZC for unthickenable special polyhedra implies AC.

The elementary move U on a simple polyhedron P consists in removing a proper butterfly E C P and replacing it by E u , see Fig. 33. u :=-=:U- i I Fig. 33. The U-move Notice that U increases the number of true vertices in a polyhedron by one, and that the Eu does not embed into R3. 9. Let P, Q be special polyhedra. Then P~Q if and only if one can transform Pinto Q by a finite sequence of moves T±I, U±1 . 11 below. 10. Let 2-dimensional polyhedra Xl, X 2 be obtained from a polyhedron Y by attaching discs Dr, D§ with homotopic attaching maps II, h : 51 ---+ Y.

It follows that W(K) does not depend on the choice of the handlebody. We have shown that any two blow-ups of K are (T, U, L)-equivalent. 21. L. Then any sequence S1, 82, ... , 8 n of elementary simplicial collapses and expansions of dimension::; 3 transforming K into L can be rearranged so that it consists of simplicial transient moves and deformations of dimension::; 2. Proof. Let Sk be the first 3-dimensional collapse in the sequence. The tetrahedron (j that disappears after 8k (together with its free triangle face 8) has been created by an expansion 8 m , Tn < k.

Download PDF sample

Algorithmic Topology and Classification of 3-Manifolds by Sergei Matveev


by William
4.3

Rated 4.93 of 5 – based on 11 votes