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Title: | Bounds on Pachner moves and systoles of cusped 3-manifolds |
Authors: | KALELKAR, TEJAS RAGHUNATH, SRIRAM Dept. of Mathematics |
Keywords: | Hauptvermutung Ideal triangulations Hyperbolic knots Pachner moves Systole length 2023-FEB-WEEK1 TOC-FEB-2023 2022 |
Issue Date: | Sep-2022 |
Publisher: | Mathematical Sciences Publishers |
Citation: | Algebraic and Geometric Topology, 22(6), 2951-2996. |
Abstract: | Any two geometric ideal triangulations of a cusped complete hyperbolic 3–manifold M are related by a sequence of Pachner moves through topological triangulations. We give a bound on the length of this sequence in terms of the total number of tetrahedra and a lower bound on dihedral angles. This leads to a naive but effective algorithm to check if two hyperbolic knots are equivalent, given geometric ideal triangulations of their complements. Given a geometric ideal triangulation of M, we also give a lower bound on the systole length of M in terms of the number of tetrahedra and a lower bound on dihedral angles. |
URI: | https://doi.org/10.2140/agt.2022.22.2951 http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/7601 |
ISSN: | 1472-2739 |
Appears in Collections: | JOURNAL ARTICLES |
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