Zobrazeno 1 - 10
of 31
pro vyhledávání: '"57M15 (primary)"'
We extend the Wirtinger number of links, an invariant originally defined by Blair et al. in terms of extending initial colorings of some strands of a diagram to the entire diagram, to spatial graphs. We prove that the Wirtinger number equals the brid
Externí odkaz:
http://arxiv.org/abs/2410.23253
In 2012, Cohen, Dasbach, and Russell presented an algorithm to construct a weighted adjacency matrix for a given knot diagram. In the case of pretzel knots, it is shown that after evaluation, the determinant of the matrix recovers the Jones polynomia
Externí odkaz:
http://arxiv.org/abs/2408.13410
Autor:
Álvarez, A., Flapan, E., Hunnell, M., Hutchens, J., Lawrence, E., Lewis, P., Price, C., Vanderpool, R.
The topological symmetry group $\mathrm{TSG}(\Gamma)$ of an embedding $\Gamma$ of a graph in $S^3$ is the subgroup of the automorphism group of the graph which is induced by homeomorphisms of $(S^3,\Gamma)$. If we restrict to orientation preserving h
Externí odkaz:
http://arxiv.org/abs/2402.08820
Autor:
Kumar, Rakesh
Let $S_g$ denote a closed oriented surface of genus $g \geq 2$. A set $\Omega = \{ c_1, \dots, c_d\}$ of pairwise non-homotopic simple closed curves on $S_g$ is called a filling system or simply a filling of $S_g$, if $S_g\setminus \Omega$ is a union
Externí odkaz:
http://arxiv.org/abs/2307.13970
Autor:
Aguillon, Yasmin, Burkholder, Eric, Cheng, Xingyu, Eddins, Spencer, Harrell, Emma, Kozai, Kenji, Leake, Elijah, Morales, Pedro
A book embedding of a complete graph is a spatial embedding whose planar projection has the vertices located along a circle, consecutive vertices are connected by arcs of the circle, and the projections of the remaining "interior" edges in the graph
Externí odkaz:
http://arxiv.org/abs/2301.02082
A theta curve is a spatial embedding of the $\theta$-graph in the three-sphere, taken up to ambient isotopy. We define the determinant of a theta curve as an integer-valued invariant arising from the first homology of its Klein cover. When a theta cu
Externí odkaz:
http://arxiv.org/abs/2211.00626
Autor:
Lappo, Egor
We define smooth notions of concordance and sliceness for spatial graphs. We prove that sliceness of a spatial graph is equivalent to a condition on a set of linking numbers together with sliceness of a link associated to the graph. This generalizes
Externí odkaz:
http://arxiv.org/abs/2205.11001
Autor:
Pavelescu, Andrei, Pavelescu, Elena
Publikováno v:
Algebr. Geom. Topol. 24 (2024) 555-568
A planar graph $G$ is said to be non-separating if there exists an embedding of $G$ in $\mathbb{R}^2$ such that for any cycle $\mathcal{C}\subset G$, all vertices of $G\setminus \mathcal{C}$ are within the same connected component of $\mathbb{R}^2\se
Externí odkaz:
http://arxiv.org/abs/2101.05740
Autor:
Douglas, Daniel C., Sun, Zhe
In a companion paper (arXiv 2011.01768), we constructed nonnegative integer coordinates $\Phi_\mathscr{T}(\mathscr{W}_{3, \hat{S}}) \subset \mathbb{Z}_{\geq 0}^N$ for the collection $\mathscr{W}_{3, \hat{S}}$ of reduced $\mathrm{SL}_3$-webs on a fini
Externí odkaz:
http://arxiv.org/abs/2012.14202
Autor:
Howie, James, Williams, Gerald
A fundamental theorem in the study of Dunwoody manifolds is a classification of finite graphs on $2n$ vertices that satisfy seven conditions (concerning planarity, regularity, and a cyclic automorphism of order $n$). Its significance is that if the p
Externí odkaz:
http://arxiv.org/abs/1905.13588