1,721,007 research outputs found
Positive braids of maximal signature
No full textWe characterise positive braid links with positive Seifert form via a finite number of forbidden minors. From this we deduce a one-to-one correspondence between prime positive braid links with positive Seifert form and simply laced Dynkin diagrams, as well as a simple classification of alternating positive braid knots
Bipartite graphs and quasipositive surfaces
Full text linkWe 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
The volume of positive braid links
Full text linkBased on recent work by Futer, Kalfagianni and Purcell, we prove that the volume of sufficiently complicated positive braid links is proportional to the signature defect Δσ = 2g−σ
Fibred links in S³
No full textWe present a simple characterization for Seifert surfaces in S³ to be fibre surfaces. As an application, we give a short topological proof of the following well-known theorem: A Murasugi sum is a fibre surface if and only if its two summands are
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