Branched Standard Spines of 3-manifolds

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.

Contenu

Motivations, plan and statements.- A review on standard spines and o-graphs.- Branched standard spines.- Manifolds with boundary.- Combed closed manifolds.- More on combings, and the closed calculus.- Framed and spin manifolds.- Branched spines and quantum invariants.- Problems and perspectives.- Homology and cohomology computations.