Download e-book for kindle: Algorithmic topology and classification of 3-manifolds by Sergei Matveev

By Sergei Matveev

ISBN-10: 3540458980

ISBN-13: 9783540458982

From the stories of the first edition:

"This e-book offers a finished and special account of other themes in algorithmic third-dimensional topology, culminating with the popularity process for Haken manifolds and together with the up to date ends up in desktop enumeration of 3-manifolds. Originating from lecture notes of varied classes given by means of the writer over a decade, the publication is meant to mix the pedagogical technique of a graduate textbook (without routines) with the completeness and reliability of a examine monograph…

All the cloth, with few exceptions, is gifted from the unusual standpoint of precise polyhedra and exact spines of 3-manifolds. This selection contributes to maintain the extent of the exposition rather straight forward.

In end, the reviewer subscribes to the citation from the again hide: "the ebook fills a spot within the latest literature and should develop into a typical reference for algorithmic three-d topology either for graduate scholars and researchers".

Zentralblatt f?r Mathematik 2004

For this 2nd version, new effects, new proofs, and commentaries for a greater orientation of the reader were additional. particularly, in bankruptcy 7 a number of new sections relating functions of the pc application "3-Manifold Recognizer" were integrated.

Show description

Read Online or Download Algorithmic topology and classification of 3-manifolds PDF

Best differential geometry books

Read e-book online An Introduction To Differential Geometry With Use Of Tensor PDF

A number of the earliest books, fairly these courting again to the 1900s and earlier than, are actually tremendous scarce and more and more pricey. we're republishing those vintage works in reasonable, prime quality, smooth variants, utilizing the unique textual content and art.

Download e-book for iPad: Parabolic Geometries I (Mathematical Surveys and Monographs) by Andreas Cap and Jan Slovak

Parabolic geometries surround a really diversified classification of geometric constructions, together with such vital examples as conformal, projective, and nearly quaternionic buildings, hypersurface kind CR-structures and diverse forms of widely used distributions. The attribute function of parabolic geometries is an identical description through a Cartan geometry modeled on a generalized flag manifold (the quotient of a semisimple Lie team by way of a parabolic subgroup).

Joseph Grifone, Zoltan Muzsnay's Variational principles for second-order differential PDF

During this publication the writer has attempted to use "a little mind's eye and pondering" to modelling dynamical phenomena from a classical atomic and molecular perspective. Nonlinearity is emphasised, as are phenomena that are elusive from the continuum mechanics standpoint. FORTRAN programmes are supplied within the appendices An creation to formal integrability idea of partial differential platforms; Frolicher-Nijenhuis thought of derivations; differential algebraic formalism of connections; important stipulations for variational sprays; obstructions to the integrability of the Euler-Lagrange procedure; the class of in the neighborhood variational sprays on two-dimensional manifolds; Euler-Lagrange structures within the isotropic case

Extra info for Algorithmic topology and classification of 3-manifolds

Example text

Namely, in a neighborhood of each edge e of K we attach a beam which runs along e and joins the blow-ups of its vertices. Denote by U the polyhedron obtained in this way. It consists of the union H of balls and beams (which is a handlebody) and of remnants of the triangles of K (which are 2-cells). Our next step consists in collapsing each ball Bv to a Bing membrane contained in it by penetrating inside Bv through two holes and exhausting the 3-dimensional material of Bv . We certainly can choose the holes in such a way that they intersect neither Dv nor the beams.

Then both of them collapse to F with a thin solid tube running along ∂F . See Fig. 37 for the genus 1 Fig. 36. Handle sliding Fig. 37. A common spine of the solid torus and solid Klein bottle 40 1 Simple and Special Polyhedra ˜ is a solid Klein bottle. To get a common case when H is a solid torus and H ˜ we collapse the tube onto a simple subpolyhedron. 19. If K is a simplicial complex, then W (K) is well defined up to (T, U, L)-equivalence. Proof. We will show step by step that arbitrary choices made by constructing W (K) (see items 1–4 above) do not affect its (T, U, L)-type.

Suppose that special polyhedra Pa and Pb are obtained from P by creating loops at a and b, respectively. Then one can transform Pa into Pb by moves T ±1 , U . Proof. We first consider the case when a and b lie in the same edge of P . Then we may assume that they coincide. 26. Suppose that Pa , Pb are obtained by two of them. Then one can transform Pa into Pb by a composition of moves β −1 , α, T −1 , and β as shown in Fig. 41. 28 to split β ±1 and α into compositions of moves T ±1 , U . If a and b lie in edges of P having a common vertex, the transformation of Pa to Pb is carried out by β −1 and β: we create a U -turn instead of the loop at a, and then replace it by a loop at b.

Download PDF sample

Algorithmic topology and classification of 3-manifolds by Sergei Matveev


by Jeff
4.4

Rated 4.95 of 5 – based on 46 votes