10 citations · 23 across the 16 of their papers we have counts for
19 papers
Computing Chebyshev knot diagrams
P. -V Koseleff, D Pecker, Fabrice Rouillier +1
A Chebyshev curve has a parametrization of the form; \ ; , where are integers, is the Chebys…
The lexicographic degree of the first two-bridge knots
Erwan Brugallé, Pierre-Vincent Koseleff, Daniel Pecker
We study the degree of polynomial representations of knots. We give the lexicographic degree of all two-bridge knots with 11 or fewer crossings. First, we estimate the total degree…
Character varieties for SL(3,C): the figure eight knot
Elisha Falbel, Antonin Guilloux, Pierre-Vincent Koseleff +2
We give a description of several representation varieties of the fundamental group of the complement of the figure eight knot in PGL(3,C) or SL(3,C). We moreover obtain an explicit…
Untangling trigonal diagrams
Erwan Brugallé, Pierre-Vincent Koseleff, Daniel Pecker
Let be a link of Conway's normal form , , or with $mn\textgreater{}0$, and let be a trigonal diagram of We show that it is possible to transfo…
On the lexicographic degree of two-bridge knots
Erwan Brugallé, Pierre-Vincent Koseleff, Daniel Pecker
We study the degree of polynomial representations of knots. We obtain the lexicographic degree for two-bridge torus knots and generalized twist knots. The proof uses the braid theo…
Local rigidity for PGL(3,C)-representations of 3-manifold groups
N. Bergeron, E. Falbel, A. Guilloux +2
Let M be a non-compact hyperbolic 3-manifold that has a triangulation by positively oriented ideal tetraedra. We explain how to produce local coordinates for the variety defined by…