Branched Standard Spines of 3-manifolds

Riccardo Benedetti, Carlo Petronio (auth.)3540626271, 9783540626275

This book provides a unified combinatorial realization of the categroies of (closed, oriented) 3-manifolds, combed 3-manifolds, framed 3-manifolds and spin 3-manifolds. In all four cases the objects of the realization are finite enhanced graphs, and only finitely many local moves have to be taken into account. These realizations are based on the notion of branched standard spine, introduced in the book as a combination of the notion of branched surface with that of standard spine. The book is intended for readers interested in low-dimensional topology, and some familiarity with the basics is assumed. A list of questions, some of which concerning relations with the theory of quantum invariants, is enclosed.

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Table of contents :
Motivations, plan and statements….Pages 1-12
A review on standard spines and o-graphs….Pages 13-22
Branched standard spines….Pages 23-39
Manifolds with boundary….Pages 40-63
Combed closed manifolds….Pages 64-72
More on combings, and the closed calculus….Pages 73-84
Framed and spin manifolds….Pages 85-97
Branched spines and quantum invariants….Pages 98-107
Problems and perspectives….Pages 108-120
Homology and cohomology computations….Pages 121-126