By Sergei Matveev

ISBN-10: 3662051028

ISBN-13: 9783662051023

ISBN-10: 3662051044

ISBN-13: 9783662051047

From the reports of the first edition:

"This booklet presents a finished and specified account of alternative subject matters in algorithmic three-d topology, culminating with the popularity process for Haken manifolds and together with the updated ends up in laptop enumeration of 3-manifolds. Originating from lecture notes of assorted classes given by way of 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 ordinary viewpoint of specific polyhedra and exact spines of 3-manifolds. This selection contributes to maintain the extent of the exposition particularly basic.

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

Zentralblatt für Mathematik 2004

For this 2^{nd} variation, new effects, new proofs, and commentaries for a greater orientation of the reader were further. particularly, in bankruptcy 7 numerous new sections pertaining to purposes of the pc software "3-Manifold Recognizer" were integrated.

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**Sample text**

22. Two marked polyhedra PI, P2 are (T, L, m)-equivalent (notation: PI T'f:J m p 2 ) if one can pass from one to the other by the following moves: (1) T±I_ and L±I-moves carried out far from the mark. This means that the mark must lie outside the fragments of P that are replaced during the moves; (2) m-move consisting of transferring the mark from one 2-cell of a bubble to another 2-cell of the same bubble. For example, if the bubble is created at a triple line, then six distinct marks on it are possible, see Fig.

The original conjecture in [3] states the following. If F is a free group on generators Xl, ... , X n , and a set {rl,"" r n} of elements of F is such that its normal closure is F, then rl, ... , r n may be transformed into Xl, ... ,X n by a finite sequence of operations of the following types: (i) (ii) (iii) (iv) replace rl by its inverse rIl; interchange rl and ri, leaving the other elements of the set unchanged; replace rl by rl r2, leaving the other elements fixed; replace rl by the conjugate grlg-l, where 9 is any element of F.

26. :Q and Q is unthickenable. , without using U- 1 . We postpone the proof to the end of this section. Let us introduce now two auxiliary moves. The first one we met earlier: it is the creation of a loop, see Fig. 32. It would be natural to call it the loop move and denote it by L, but L is occupied by the lune move. So we adopt the above name and denote the loop move by a considering the shape of the letter as a motivation. 27. The loop move transforms a regular neighborhood of a triple point that consists of three half-discs with a common diameter.

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