Zobrazeno 1 - 10
of 446
pro vyhledávání: '"Dancsó A"'
A complete Reidemeister characterisation of welded links is a long-standing open problem. We present a Reidemeister Theorem for a related class of four-dimensional links, solid ribbon torus links: immersed solid tori in R4 with only ribbon singularit
Externí odkaz:
http://arxiv.org/abs/2407.02734
We show that solutions to the Kashiwara-Vergne problem can be extended degree by degree. This can be used to simplify the computation of a class of Drinfel'd associators, which under the Alekseev-Torossian conjecture, may comprise all associators. We
Externí odkaz:
http://arxiv.org/abs/2310.20420
In this paper, we study alternating links in thickened surfaces in terms of the lattices of integer flows on their Tait graphs. We use this approach to give a short proof of the first two generalised Tait conjectures. We also prove that the flow latt
Externí odkaz:
http://arxiv.org/abs/2306.08971
Homomorphic expansions are combinatorial invariants of knotted objects, which are universal in the sense that all finite-type (Vassiliev) invariants factor through them. Homomorphic expansions are also important as bridging objects between low-dimens
Externí odkaz:
http://arxiv.org/abs/2211.11370
Publikováno v:
In Carbohydrate Polymers 1 January 2025 347
Autor:
Dancso, Zsuzsanna, Lim, Jongmin
A 2010 result of Amini provides a way to extract information about the structure of the graph from the geometry of the Voronoi polytope of the lattice of integer flows (which determines the graph up to two-isomorphism). Specifically, Amini shows that
Externí odkaz:
http://arxiv.org/abs/2202.13265
Autor:
Brand, Jack, Burton, Benjamin A., Dancso, Zsuzsanna, He, Alexander, Jackson, Adele, Licata, Joan
Publikováno v:
Discrete Comput. Geom. 71, 1190-1209 (2024)
We develop a theory of link projections to trivalent spines of 3-manifolds. We prove a Reidemeister Theorem providing a set of combinatorial moves sufficient to relate the projections of isotopic links. We also show that any link admits a crossingles
Externí odkaz:
http://arxiv.org/abs/2202.02007
In 2017 Bar-Natan and the first author showed that solutions to the Kashiwara--Vergne equations are in bijection with certain knot invariants: homomorphic expansions of welded foams. Welded foams are a class of knotted tubes in $\mathbb{R}^4$, which
Externí odkaz:
http://arxiv.org/abs/2106.02373
Circuit algebras, introduced by Bar-Natan and the first author, are a generalization of Jones's planar algebras, in which one drops the planarity condition on "connection diagrams". They provide a useful language for the study of virtual and welded t
Externí odkaz:
http://arxiv.org/abs/2009.09738
Over-then-Under (OU) tangles are oriented tangles whose strands travel through all of their over crossings before any under crossings. In this paper we discuss the idea of gliding: an algorithm by which any tangle diagram could be brought to OU form.
Externí odkaz:
http://arxiv.org/abs/2007.09828