Displaying similar documents to “Quantum invariants of links and 3-valent graphs in 3-manifolds”

Dotted links, Heegaard diagrams, and colored graphs for PL 4-manifolds.

Maria Rita Casali (2004)

Revista Matemática Complutense

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The present paper is devoted to establish a connection between the 4-manifold representation method by dotted framed links (or -in the closed case- by Heegaard diagrams) and the so called crystallization theory, which visualizes general PL-manifolds by means of edge-colored graphs. In particular, it is possible to obtain a crystallization of a closed 4-manifold M4 starting from a Heegaard diagram (#m(S1 x S2...

An equivalence criterion for 3-manifolds.

M. R. Casali (1997)

Revista Matemática de la Universidad Complutense de Madrid

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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.

A TQFT for Wormhole cobordisms over the field of rational functions

Patrick Gilmer (1998)

Banach Center Publications

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We consider a cobordism category whose morphisms are punctured connected sums of S 1 × S 2 ’s (wormhole spaces) with embedded admissibly colored banded trivalent graphs. We define a TQFT on this cobordism category over the field of rational functions in an indeterminant A. For r large, we recover, by specializing A to a primitive 4rth root of unity, the Witten-Reshetikhin-Turaev TQFT restricted to links in wormhole spaces. Thus, for r large, the rth Witten-Reshetikhin-Turaev invariant of a link...