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Delta link-homotopy on spatial graphs.

Ryo Nikkuni (2002)

Revista Matemática Complutense

We study new equivalence relations in spatial graph theory. We consider natural generalizations of delta link-homotopy on links, which is an equivalence relation generated by delta moves on the same component and ambient isotopies. They are stronger than edge-homotopy and vertex-homotopy on spatial graphs which are natural generalizations of link-homotopy on links. Relationship to existing familiar equivalence relations on spatial graphs are stated, and several invariants are defined by using the...

Discrete Dirac operators on Riemann surfaces and Kasteleyn matrices

David Cimasoni (2012)

Journal of the European Mathematical Society

Let $\sum$ be a flat surface of genus $g$ with cone type singularities. Given a bipartite graph $Γ$ isoradially embedded in $\sum$ , we define discrete analogs of the $2^{2 g}$ Dirac operators on $\sum$ . These discrete objects are then shown to converge to the continuous ones, in some appropriate sense. Finally, we obtain necessary and sufficient conditions on the pair $Γ \subset \sum$ for these discrete Dirac operators to be Kasteleyn matrices of the graph $Γ$ . As a consequence, if these conditions are met, the partition function of the dimer...

Discrete Morse inequalities on infinite graphs.

Ayala, Rafael, Fernández, Luis M., Vilches, José A. (2009)

The Electronic Journal of Combinatorics [electronic only]

Discrete Morse theory and graph braid groups.

Farley, Daniel, Sabalka, Lucas (2005)

Algebraic & Geometric Topology

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

Maria Rita Casali (2004)

Revista Matemática Complutense

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),ω) and the algorithmicity of the whole process depends on the effective possibility of recognizing...

Double coverings and reflexive abelian hypermaps.

Breda d'Azevedo, Antonio J., Jones, Gareth A. (2000)

Beiträge zur Algebra und Geometrie