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pro vyhledávání: '"Menasco, William W."'
Autor:
Alegria, Linda V., Menasco, William W.
From classical knot theory we know that every knot in $S^3$ is the boundary of an oriented, embedded surface. A standard demonstration of this fact achieved by elementary technique comes from taking a regular projection of any knot and employing Seif
Externí odkaz:
http://arxiv.org/abs/2405.14805
Autor:
Menasco, William W., Solanki, Deepisha
Our main results concern changing an arbitrary plat presentation of a split or composite link to one which is obviously recognizable as being split or composite. Pocket moves, first described in \cite{unlinkviaplats}, are utilized -- a pocket move al
Externí odkaz:
http://arxiv.org/abs/2402.09669
Autor:
Chang, Hong, Menasco, William W.
Let $S_g$ denote the genus $g$ closed orientable surface. A \emph{coherent filling pair} of simple closed curves, $(\alpha,\beta)$ in $S_g$, is a filling pair that has its geometric intersection number equal to the absolute value of its algebraic int
Externí odkaz:
http://arxiv.org/abs/2302.03632
Autor:
Menasco, William W., Nichols, Margaret
This is an investigation into a classification of embeddings of a surface in Euclidean $3$-space. Specifically, we consider $\mathbb{R}^3$ as having the product structure $\mathbb{R}^2 \times \mathbb{R}$ and let $\pi:\mathbb{R}^2 \times \mathbb{R} \t
Externí odkaz:
http://arxiv.org/abs/2206.06542
Autor:
Jin, Xifeng, Menasco, William W.
We show that efficient geodesics have the strong property of "super efficiency". For any two vertices, $v , w \in \mathcal{C}(S_g)$, in the complex of curves of a closed oriented surface of genus $g \geq 2 $, and any efficient geodesic, $v = v_1 , \c
Externí odkaz:
http://arxiv.org/abs/2008.09665
An "origami" (or flat structure) on a closed oriented surface, $S_g$, of genus $g \geq 2$ is obtained from a finite collection of unit Euclidean squares by gluing each right edge to a left one and each top edge to a bottom one. The main objects of st
Externí odkaz:
http://arxiv.org/abs/2008.09179
Autor:
Menasco, William W.
This is a short expository article on alternating knots and is to appear in the Concise Encyclopedia of Knot Theory.
Comment: 12 pages, 11 figures
Comment: 12 pages, 11 figures
Externí odkaz:
http://arxiv.org/abs/1901.00582
Publikováno v:
In Topology and its Applications 1 July 2021 298
The complex of curves $\mathcal{C}(S_g)$ of a closed orientable surface of genus $g \geq 2$ is the simplicial complex having its vertices, $\mathcal{C}^0(S_g)$, are isotopy classes of essential curves in $S_g$. Two vertices co-bound an edge of the $1
Externí odkaz:
http://arxiv.org/abs/1408.4134
Publikováno v:
Algebr. Geom. Topol. 14 (2014) 3589-3601
We show that after stabilizations of opposite parity and braid isotopy, any two braids in the same topological link type cobound embedded annuli. We use this to prove the generalized Jones conjecture relating the braid index and algebraic length of c
Externí odkaz:
http://arxiv.org/abs/1302.1247