arXiv research

Character varieties get a natural Poisson structure.

Quantum character varieties unify four construction methods.

Character variety of Borromean link solved, Alexander polynomial formula found.

Computes dimensions of representation and character varieties for 2 and 3-dimensional orbifolds.

Researchers describe character varieties for Hopf links, proving geometric properties.

Character variety of Whitehead link described in detail.

Proves Torelli group action is ergodic on Lie group character varieties.

We study some basic properties of the variety of characters in PSL(2,C) of a finitely generated group. In particular we give an interpretation of its points as characters of representations. We construct 3-manifolds whose variety of characters has arbitrarily many components that do not lift to SL(2,C). We also study t…

Study $\mathrm{SL}_2(\mathbb{F})$-character varieties of knots over fields of odd characteristic.

The paper extends character varieties to marked surfaces and discovers their triangular decompositions.

Detecting essential surfaces in 3-manifolds and orbifolds using character varieties.

Quantum trace maps abelian character varieties to SL2 character varieties.

Finite automorphisms of SL(2,C) character varieties identified.

A family of new algebraic Poisson varieties will be constructed, generalising the complex character varieties of Riemann surfaces. Then the well-known (Poisson) mapping class group actions on the character varieties will be generalised.

Study character varieties of hyperbolic 3-manifolds using bundle methods.

Study of pseudo-Anosov actions on $SU(2)$-character variety for genus 2 surfaces.

The powerful character variety techniques of Culler and Shalen can be used to find essential surfaces in knot manifolds. We show that module structures on the coordinate ring of the character variety can be used to identify detected boundary slopes as well as when closed surfaces are detected. This approach also yields…

Study of SU(2,1) character varieties on one-holed torus.

Character varieties of knot groups into SU(3) are stratified and analyzed.

New compactification for character varieties with good topological properties.

Study character varieties of arborescent knots and hyperbolic knots.

Study character variety of a special 3-manifold, finding a polynomial formula.

Let $Γ$ be a finitely generated group and $G$ a real form of $\mathrm{SL}_n(\mathbb{C})$. We propose a definition for the $G$-character variety of $Γ$ as a subset of the $\mathrm{SL}_n(\mathbb{C})$-character variety of $Γ$. We consider two anti-holomorphic involutions of the $\mathrm{SL}_n(\mathbb{C})$ character variet…

We describe the (P)SL(2,C) character varieties of all 2-bridge knots and the diagonal character varieties for all 2-bridge links in terms of a set of polynomials defined using Farey recursion.

Minimal action of mapping class group on character variety.

Anosov representations of surface groups are complex manifolds.

In this paper we consider some families of links, including (-2,2m+1,2n)-pretzel links and twisted Whitehead links. We calculate the character varieties of these families, and determine the number of irreducible components of these character varieties.

We describe a birational map between subvarieties in the character varieties of mutative 3-manifolds. By studying the birational map, one can decide in certain circumstances whether a mutation surface is detected by an ideal point of the character variety.

The paper studies compactifications of SL(2,C) character varieties for punctured surfaces.

We will construct twisted versions of the wild character varieties.

Study shows how certain knots and tori are detected by ideal points in character varieties.

Study of twisted $L^2$-torsion on 3-manifold character varieties.

Authors determine the SL(2,C) character variety of a specific knot without computer aid.

Compactifies character varieties for group actions.

New method to compute tangle sums in character varieties.

We show that for any knot there exist only finitely many irreducible metabelian characters in the $SL(2,\mathbb{C})$-character variety of the knot group, and the number is given explicitly by using the determinant of the knot. Then it turns out that for any 2-bridge knot a section of the $SL(2,\mathbb{C})$-character va…

Researchers describe the dual of cohomology generators for SU(2) character varieties of surfaces.

The paper calculates the motive of a specific knot's character variety.

Classifies invariant measures on specific character varieties.

In this paper we define the adjoint Reidemeister torsion as a differential form on the character variety of a compact oriented 3-manifold with toral boundary, and prove it defines a regular volume form. Then we show that the torsion form can vanish only at singular points of the character variety. In fact, if the singu…

These lecture notes concern the algebraic geometry of the character variety of a finitely generated group in SL(2,C) from the point of view of skein modules. We focus on the case of surface and 3-manifolds groups and construct the Reidemeister torsion as a rational volume form on the character variety.

Method determines SL(2,C) character variety for Montesinos knots.

It has been an open question whether all boundary slopes of hyperbolic knots are strongly detected by the character variety. The main result of this paper produces an infinite family of hyperbolic knots each of which has at least one strict boundary slope that is not strongly detected by the character variety.

3D hyperbolic manifolds map one-to-one to their boundary character varieties.

Character varieties of prime knots have high-dimensional components.

Let M be an orientable, cusped hyperbolic 3-manifold of finite volume. We show that the restriction map from a Dehn surgery component in the PSL(2,C)-character variety of M to the character variety of the boundary of M is a birational isomorphism onto its image. This generalises a result by Nathan Dunfield. A key step …

We study the (relative) SL(2,C) character varieties of the three-holed projective plane and the action of the mapping class group on them. We describe a domain of discontinuity for this action, which strictly contains the set of primitive stable representations defined by Minsky, and also the set of convex-cocompact ch…

Defines character varieties for real forms of complex classical groups and proves their properties.