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pro vyhledávání: '"Burton Benjamin"'
We present a framework to classify PL-types of large censuses of triangulated $4$-manifolds, which we use to classify the PL-types of all triangulated $4$-manifolds with up to $6$ pentachora. This is successful except for triangulations homeomorphic
Externí odkaz:
http://arxiv.org/abs/2412.04768
Autor:
Burton, Benjamin A., Thompson, Finn
The Heegaard genus is a fundamental invariant of 3-manifolds. However, computing the Heegaard genus of a triangulated 3-manifold is NP-hard, and while algorithms exist, little work has been done in making such an algorithm efficient and practical for
Externí odkaz:
http://arxiv.org/abs/2403.11659
The operation of crushing a normal surface has proven to be a powerful tool in computational $3$-manifold topology, with applications both to triangulation complexity and to algorithms. The main difficulty with crushing is that it can drastically cha
Externí odkaz:
http://arxiv.org/abs/2403.11523
Autor:
Burton, Benjamin A., He, Alexander
Publikováno v:
39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 21:1-21:16, 2023
We often rely on censuses of triangulations to guide our intuition in $3$-manifold topology. However, this can lead to misplaced faith in conjectures if the smallest counterexamples are too large to appear in our census. Since the number of triangula
Externí odkaz:
http://arxiv.org/abs/2303.06321
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
Autor:
Burton, Benjamin A., Chang, Hsien-Chih, Löffler, Maarten, de Mesmay, Arnaud, Maria, Clément, Schleimer, Saul, Sedgwick, Eric, Spreer, Jonathan
We present three "hard" diagrams of the unknot. They require (at least) three extra crossings before they can be simplified to the trivial unknot diagram via Reidemeister moves in $\mathbb{S}^2$. Both examples are constructed by applying previously p
Externí odkaz:
http://arxiv.org/abs/2104.14076
Autor:
Burton, Benjamin A., He, Alexander
A key result in computational 3-manifold topology is that any two triangulations of the same 3-manifold are connected by a finite sequence of bistellar flips, also known as Pachner moves. One limitation of this result is that little is known about th
Externí odkaz:
http://arxiv.org/abs/2012.02398
Autor:
Burton, Benjamin A., He, Alexander
Publikováno v:
J. Appl. Comput. Topol. 5 (2021) 583-619
For many fundamental problems in computational topology, such as unknot recognition and $3$-sphere recognition, the existence of a polynomial-time solution remains unknown. A major algorithmic tool behind some of the best known algorithms for these p
Externí odkaz:
http://arxiv.org/abs/1912.09051
In this paper, we study knot diagrams for which the underlying graph has treewidth two. We give a linear time algorithm for the following problem: given a knot diagram of treewidth two, does it represent the unknot? We also show that for a link diagr
Externí odkaz:
http://arxiv.org/abs/1904.03117
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