127 research outputs found
Dessins d'enfants for analysts
We present an algorithmic way of exactly computing Belyi functions for
hypermaps and triangulations in genus 0 or 1, and the associated dessins, based
on a numerical iterative approach initialized from a circle packing combined
with subsequent lattice reduction. The main advantage compared to previous
methods is that it is applicable to much larger graphs; we use very little
algebraic geometry, and aim for this paper to be as self-contained as possible
Twisted Alexander polynomials and incompressible surfaces given by ideal points
We study incompressible surfaces constructed by Culler-Shalen theory in the
context of twisted Alexander polynomials. For a st cohomology class of a
-manifold the coefficients of twisted Alexander polynomials induce regular
functions on the -character variety. We prove that if an
ideal point gives a Thurston norm minimizing non-separating surface dual to the
cohomology class, then the regular function of the highest degree has a finite
value at the ideal point.Comment: 10 pages, to appear in "The special issue for the 20th anniversary",
the Journal of Mathematical Sciences, the University of Toky
- …