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As a generalization of the classical knots, knotoids are equivalence classes of immersions of the oriented unit interval in a surface. In recent years, a variety of invariants of spherical and planar knotoids have been constructed as extensions of in
Externí odkaz:
http://arxiv.org/abs/2412.19554
Autor:
Chen, Qingtao, Zhu, Shengmao
In this article, we obtain an asymptotic expansion formula for the relative Reshetikhin-Turaev invariant in the case that the ambient 3-manifold is gained by doing rational surgery along one component of Whitehead link. In addition, we obtain an asym
Externí odkaz:
http://arxiv.org/abs/2412.10868
In this paper, we tabulate the set of alternating pretzel links. Specifically, for any given crossing number $c$, we derive a closed formula that would allow us to compute $\mathcal{P}(c)$, the total number of alternating pretzel links with crossing
Externí odkaz:
http://arxiv.org/abs/2412.06103
Autor:
Manturov, Vassily Olegovich
In the present paper, we construct an invariant of braids in the real projective plane which corresponds to an ``action'' of braids on certain graphs in $\R{}P^{2}$ with labels. This paper is a sequel of papers \cite{M},\cite{KM}. It demonstrates onc
Externí odkaz:
http://arxiv.org/abs/2411.18991
Infinite families of 3-dimensional closed graph manifolds and closed Seifert fibered spaces are exhibited, each member of which contains an essential torus not detected by ideal points of the variety of $\text{SL}_2(\mathbb{F})$-characters over any a
Externí odkaz:
http://arxiv.org/abs/2411.15680
Autor:
Garden, Grace S., Tillmann, Stephan
In the seminal work of Culler and Shalen from 1983, essential surfaces in 3-manifolds are associated to ideal points of their $\text{SL}_2(\mathbb{C})$-character varieties, and connections between the algebraic geometry of the character variety and t
Externí odkaz:
http://arxiv.org/abs/2411.06859
Howards and Kobin give a sharp upper bound for crossing number of knots on rectangular mosaics. Here we extend the proof to create a new bound for hexagonal mosaics in all three natural settings and shorten the proof in the rectangular setting.
Externí odkaz:
http://arxiv.org/abs/2410.19570
Autor:
Popova, D. A.
Maps from links in thickened surfaces to flat-virtual links help to construct invariants of links using invariants of flat-virtual links. This work is dedicated to investigation of equivalence and invariants of flat-virtual diagrams obtained as image
Externí odkaz:
http://arxiv.org/abs/2410.04517
Autor:
Buccoliero, Fabio, Barthel, Senja
Leveled spatial graphs are studied regarding other spatial graph properties, including being free or paneled. New graph invariants are defined for an abstract graph permitting a leveled embedding: the level number and the hamiltonian level number for
Externí odkaz:
http://arxiv.org/abs/2409.14974
Surgery on a knot in $S^3$ is said to be an alternating surgery if it yields the double branched cover of an alternating link. The main theoretical contribution is to show that the set of alternating surgery slopes is algorithmically computable and t
Externí odkaz:
http://arxiv.org/abs/2409.09842