相关论文: The SL(2,C) character variety of the one-holed tor…

In this manuscript we consider a special complex torus, denoted $S_{\Delta_{2k}}$ (for each $k \in \mathbb{N},\, k \geq 1$) and called the Dirac spinor torus. It is an Abelian variety of complex dimension $2^{k}$ whose covering space is the…

Let Mod(S) be the extended mapping class group of a surface S. For S the twice-punctured torus, we show that there exists an isomorphism of finite index subgroups of Mod(S) which is not the restriction of an inner automorphism. For S a…

Let $(X, \omega)$ be a conical symplectic variety of dimension $2n$ which has a projective symplectic resolution. Assume that $X$ admits an effective Hamiltonian action of an $n$-dimensional algebraic torus $T^n$, compatible with the…

Let K be a knot in an integral homology 3-sphere and let B denote the 2-fold branched cover of the integral homology sphere branched along K. We construct a map from the slice of characters with trace free along meridians in the SL(2,…

Let pi be a free group of rank 2. Its outer automorphism group Out(pi) acts on the space of equivalence classes of representations in Hom(pi, SL(2,C)). Let SLm(2,R) denote ths subset of GL(2,R) consisting of matrices of determinant -1 and…

We show that for a torus knot the SL(2;C) Chern-Simons invariants and the SL(2;C) twisted Reidemeister torsions appear in an asymptotic expansion of the colored Jones polynomial. This suggests a generalization of the volume conjecture that…

All bicovariant first order differential calculi on the quantum group GLq(3,C) are determined. There are two distinct one-parameter families of calculi. In terms of a suitable basis of 1-forms the commutation relations can be expressed with…

Let M be a compact, orientable, hyperbolizable 3-manifold with incompressible boundary which is not an interval bundle. We study the dynamics of the action of the outer automorphism group of the fundamental group of M on the relative…

We calculate the E-polynomials of certain twisted GL(n,C)-character varieties M_n of Riemann surfaces by counting points over finite fields using the character table of the finite group of Lie-type GL(n,F_q) and a theorem proved in the…

We consider two sign characters defined on a tamely ramified maximal torus T of a twisted Levi subgroup M of a reductive p-adic group G. We show that their product extends to the stabilizer M(F)_x of any point x in the Bruhat-Tits building…

We extend the computations in [AGM1, AGM2, AGM3] to find the cohomology in degree five of a congruence subgroup Gamma of SL(4,Z) with coefficients in a field K, twisted by a nebentype character eta, along with the action of the Hecke…

An SL(2, Z) family of string solutions of type IIB supergravity in ten dimensions is constructed. The solutions are labeled by a pair of relatively prime integers, which characterize charges of the three-form field strengths. The string…

We study the space of slice-torus invariants. In particular we characterize the set of values that slice-torus invariants may take on a given knot in terms of the stable smooth slice genus. Our study reveals that the resolution of the local…

We evaluate characters of irreducible representations of the N=2 supersymmetric extension of the Virasoro algebra. We do so by deriving the BGG-resolution of the admissible N=2 representations and also a new 3,5,7...-resolution in terms of…

Kontsevich and Soibelman defined Donaldson-Thomas invariants of a 3d Calabi-Yau category equipped with a stability condition. Any cluster variety gives rise to a family of such categories. Their DT invariants are encapsulated in a single…

Using exhaustion properties of invariant plurisubharmonic functions along with basic combinatorial information on toric varieties convergence results for sequences of distribution functions \phi_n=|s_N| / |s_N|_{L^2} for sections s_N\in…

The torus group $(S^1)^{\ell+1}$ has a canonical action on the odd dimensional sphere $S_q^{2\ell+1}$. We take the natural Hilbert space representation where this action is implemented and characterize all odd spectral triples acting on…

We study affine toric varieties with an action of group $SL_n$ with a dense orbit. A characterisation in terms of $SL_n \times Q$-modules is given where $Q$ is a quasitorus. This characterisation is more explicitly expanded in case $n=3$.…

Let $k$ be a finitely generated field of characteristic $p>0$ and $X$ a smooth and proper scheme over $k$. Recent works of Cadoret, Hui and Tamagawa show that, if $X$ satisfies the $\ell$-adic Tate conjecture for divisors for every prime…

Using the theory of perverse sheaves of vanishing cycles, we define a homological invariant of knots in three-manifolds, similar to the three-manifold invariant constructed by Abouzaid and the second author. We use spaces of SL(2,C) flat…