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An equivalence criterion for 3-manifolds.

M. R. Casali (1997)

Revista Matemática de la Universidad Complutense de Madrid

Within geometric topology of 3-manifolds (with or without boundary), a representation theory exists, which makes use of 4-coloured graphs. Aim of this paper is to translate the homeomorphism problem for the represented manifolds into an equivalence problem for 4-coloured graphs, by means of a finite number of graph-moves, called dipole moves. Moreover, interesting consequences are obtained, which are related with the same problem in the n-dimensional setting.

An introduction to the abelian Reidemeister torsion of three-dimensional manifolds

Gwénaël Massuyeau (2011)

Annales mathématiques Blaise Pascal

These notes accompany some lectures given at the autumn school “Tresses in Pau” in October 2009. The abelian Reidemeister torsion for 3 -manifolds, and its refinements by Turaev, are introduced. Some applications, including relations between the Reidemeister torsion and other classical invariants, are surveyed.

Around the Borromean link.

José María Montesinos Amilibia (2008)

RACSAM

This is a survey of some consequences of the fact that the fundamental group of the orbifold with singular set the Borromean link and isotropy cyclic of order 4 is a universal kleinian group.

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