Bipartite graphs and combinatorial adjacency
Sebastian Baader
TL;DR
This paper introduces a combinatorial model using bipartite graphs for quasipositive surfaces and positive braids, extending duality in torus links and exploring adjacency in bipartite graph links related to plane curve singularities.
Contribution
It presents a new combinatorial framework for quasipositive surfaces and positive braids, extending duality concepts and proposing a notion of adjacency for bipartite graph links.
Findings
Extended duality on torus link diagrams to twisted torus links
Introduced a combinatorial notion of adjacency for bipartite graph links
Discussed potential connections with plane curve singularities
Abstract
We present a simple combinatorial model for quasipositive surfaces and positive braids, based on embedded bipartite graphs. As a first application, we extend the well-known duality on standard diagrams of torus links to twisted torus links. We then introduce a combinatorial notion of adjacency for bipartite graph links and discuss its potential relation with the adjacency problem for plane curve singularities.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Homotopy and Cohomology in Algebraic Topology