Zobrazeno 1 - 10
of 191
pro vyhledávání: '"A. Heusener"'
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 representation variety at these diagonal representations, and show that th
Externí odkaz:
http://arxiv.org/abs/2404.09548
Autor:
Heusener, Michael, Porti, Joan
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 $\Gamma$, we give equations defining the coordinate ring of the scheme of SL(2,C)-characters of $\Gamma
Externí odkaz:
http://arxiv.org/abs/2210.13888
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 behavior of these twisted Alexander polynomials evaluated at unit complex nu
Externí odkaz:
http://arxiv.org/abs/1912.12946
Autor:
Heusener, Michael, Weidmann, Richard
Publikováno v:
J. Group Theory 22 (2019), no. 1, 15-21
We observe that Whitehead's lemma is an immediate consequence of Stallings folds.
Externí odkaz:
http://arxiv.org/abs/1805.12357
Autor:
Heusener, Michael, Porti, Joan
Publikováno v:
Annales Henri Lebesgue, UFR de Math{\'e}matiques - IRMAR, 2020, 3, pp.341-380
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 group. One of the forms is a Reidemeister torsion, the other one is t
Externí odkaz:
http://arxiv.org/abs/1804.07504
Autor:
Friedl, Stefan, Heusener, Michael
Publikováno v:
Algebr. Geom. Topol. 18 (2018) 313-332
Given a hyperbolic knot $K$ and any $n\geq 2$ the abelian representations and the holonomy representation each give rise to an $(n-1)$-dimensional component in the $\operatorname{SL}(n,\Bbb{C})$-character variety. A component of the $\operatorname{SL
Externí odkaz:
http://arxiv.org/abs/1610.04414
Autor:
Heusener, Michael, Zentner, Raphael
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 group. An essential input is a recent result of the second author, st
Externí odkaz:
http://arxiv.org/abs/1610.04092
Autor:
Heusener, Michael
The first part of this article is a general introduction to the the theory of representation spaces of discrete groups into SL(n,C). Special attention is paid to knot groups. In Section 2 we discuss the difference between the tangent space at the rep
Externí odkaz:
http://arxiv.org/abs/1602.03825
We give explicit equations that describe the character variety of the figure eight knot for the groups SL(3,C), GL(3,C) and PGL(3,C). This has five components of dimension 2, one consisting of totally reducible representations, another one consisting
Externí odkaz:
http://arxiv.org/abs/1505.04451
The aim of this article is to study the existence of certain reducible, metabelian representations of knot groups into $\mathrm{SL}(n,\mathbf{C})$ which generalise the representations studied previously by G.~Burde and G.~de Rham. Under specific hypo
Externí odkaz:
http://arxiv.org/abs/1502.03999