New geometric triangulations for complements of twist knots
Aribi, Fathi Ben ; Piguet-Nakazawa, Eiichi
arXiv, Tome 2019 (2019) no. 0, / Harvested from
We construct a new infinite family of ideal triangulations for the complements of the twist knots, using a method of Thurston. These triangulations provide a new upper bound for the Matveev complexity of the twist knot complements. Furthermore, we prove that these triangulations are geometric when the twist knots have an odd number of crossings. The proof uses techniques of Futer and Gu\'eritaud, which consist in studying the volume functional on the polyhedron of angle structures.
Publié le : 2019-03-22
Classification:  Mathematics - Geometric Topology,  57M25, 57M27, 57M50 
@article{1903.09480,
     author = {Aribi, Fathi Ben and Piguet-Nakazawa, Eiichi},
     title = {New geometric triangulations for complements of twist knots},
     journal = {arXiv},
     volume = {2019},
     number = {0},
     year = {2019},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1903.09480}
}

Aribi, Fathi Ben; Piguet-Nakazawa, Eiichi. New geometric triangulations for complements of twist knots. arXiv, Tome 2019 (2019) no. 0, . http://gdmltest.u-ga.fr/item/1903.09480/