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Alexander ideals of classical knots.

Cherry Kearton, Stephen M. J. Wilson (1997)

Publicacions Matemàtiques

The Alexander ideals of classical knots are characterised, a result which extends to certain higher dimensional knots.

Algebraic properties of decorated splitting obstruction groups

A. Cavicchioli, Y. V. Muranov, D. Repovš (2001)

Bollettino dell'Unione Matematica Italiana

In questo articolo si riassumono le definizioni e le principali proprietà dei gruppi di ostruzione con decorazione di tipo LS e LP. Si stabiliscono nuove relazioni fra questi gruppi e si descrivono le proprietà delle mappe naturali fra differenti gruppi con decorazione. Si costruiscono varie successioni spettrali, contenenti questi gruppi con decorazione, e si studiano la loro connessione con le successioni spettrali in K -teoria per certe estensioni quadratiche di antistrutture. Infine, si introduce...

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.

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