31 citations · 101 across the 17 of their papers we have counts for
15 papers · 1 filter
On the local structure of the SL(n,C)-representation variety of knot groups
Michael Heusener, Leila Ben Abdelghani
We study the local structure of the representation variety of a knot group into SL(n,C) at certain diagonal representations. In particular we determine the tangent cone of the repr…
The scheme of characters in SL 2
Michael Heusener, Joan Porti
The aim of this article is to study the SL(2,C)-character scheme of a finitely generated group. Given a presentation of a finitely generated group , we give equations defining t…
Asymptotics of twisted Alexander polynomials and hyperbolic volume
Léo Bénard, Jérôme Dubois, Michael Heusener +1
For a hyperbolic knot and a natural number n, we consider the Alexander polynomial twisted by the n-th symmetric power of a lift of the holonomy. We establish the asymptotic behavi…
Holomorphic volume forms on representation varieties of surfaces with boundary
Michael Heusener, Joan Porti
For closed and oriented hyperbolic surfaces, a formula of Witten establishes an equality between two volume forms on the space of representations of the surface in a semisimple Lie…
On high-dimensional representations of knot groups
Stefan Friedl, Michael Heusener
Given a hyperbolic knot and any the abelian representations and the holonomy representation each give rise to an -dimensional component in the $\operatorname{S…
A new algorithm for 3-sphere recognition
Michael Heusener, Raphael Zentner
We prove the existence of a new algorithm for 3-sphere recognition based on Groebner basis methods applied to the variety of $\text{\em SL}(2,\C)$-representation of the fundamental…