3,496 research outputs found
Positive braids of maximal signature
We 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.Comment: 7 pages, 7 figure
Asymptotic Rasmussen Invariant
We use simple properties of the Rasmussen invariant of knots to study its
asymptotic behaviour on the orbits of a smooth volume preserving vector field
on a compact domain in the 3-space. A comparison with the asymptotic signature
allows us to prove that asymptotic knots are non-alternating, in general.
Further we show that the Rasmussen invariant defines a quasi-morphism on the
braid groups and derive estimates for the stable commutator and torsion lengths
of alternating braids.Comment: 12 pages, 5 figure
Scissor equivalence for torus links
This article is about a natural distance function induced by smooth
cobordisms between links. We show that the cobordism distance of torus links is
determined by the profiles of their signature functions, up to a constant
factor.Comment: 15 pages, 5 figures, Theorem 1 adde
The volume of positive braid links
Based 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 .Comment: 4 page
Slice and Gordian numbers of track knots
We present a class of knots associated with labelled generic immersions of
intervals into the plane and compute their Gordian numbers and 4-dimensional
invariants. At least 10% of the knots in Rolfsen's table belong to this class
of knots. We call them track knots. They are contained in the class of
quasipositive knots. In this connection, we classify quasipositive knots and
strongly quasipositive knots up to 10 crossings.Comment: 16 pages, 17 figure
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