Related papers: Topological Representations of $U_q(sl_2)$ on the …
We study representations of the mapping class group of the punctured torus on the double of a finite dimensional possibly non-semisimple Hopf algebra that arise in the construction of universal, extended topological field theories. We…
We describe the action of the automorphism group of the complex cubic x^2+y^2+z^2-xyz-2 on the homology of its fibers. This action includes the action of the mapping class group of a punctured torus on the subvarieties of its SL(2,C)…
In this paper we consider the action of the mapping class group of a surface on the space of homomorphisms from the fundamental group of a surface into PSL(2,R). Goldman conjectured that when the surface is closed and of genus bigger than…
We calculate the virtually-cyclic dimension of the mapping class group of a sphere with at most six punctures. As an immediate consequence, we obtain the virtually-cyclic dimension of the mapping class group of the twice-holed torus and of…
In this paper we examine the topology of manifolds equipped with a local quaternionic toric action modeled on the regular representation of the quaternionic torus $Q^n=(S^3)^n$. Building on our previous work, where the toric, differential…
We describe the action of the mapping class group $M(g,n)$ on the fundamental group of $T_{g,n}$, a compact orientable topological surface of positive genus $g$ with $n$ marked points. This is achieved by computing the image of the…
We show that the structure of the Liouville action on a two dimensional Regge surface of the topology of the sphere and of the torus is determined by the invariance under the transformations induced by the conformal Killing vector fields…
The paper exhibits a product-to-sum formula for the observables of a certain quantization of the moduli space of flat SU(2)-connections on the torus. This quantization was defined using the topological quantum field theory that was…
Let $X$ be a $2n$-manifold with a locally standard action of a compact torus $T^n$. If the free part of action is trivial and proper faces of the orbit space $Q$ are acyclic, then there are three types of homology classes in $X$: (1)…
Let X_n be a cycle of n projective lines, and T_n a symplectic torus with n punctures. In this paper we review results appeared in arXiv:1103.2462 and in arXiv:1109.6615, which establish a version of homological mirror symmetry relating X_n…
Rational conformal field theories produce a tower of finite-dimensional representations of surface mapping class groups, acting on the conformal blocks of the theory. We review this formalism. We show that many recent mathematical…
We present a complete classification of elements in the mapping class group of the torus which have a representative that can be written as a product of two orientation reversing involutions. Our interest in such decompositions is motivated…
Using gauge theory and functional integral methods, we derive concrete expressions for the partition functions of BF theory and the U(1|1) model of Rozansky and Saleur on $\Sigma x S^{1}$, both directly and using equivalent two-dimensional…
The moduli space of flat SL(2,R)-connections modulo gauge transformations on the torus may be described by ordered pairs of commuting SL(2,R) matrices modulo simultaneous conjugation by SL(2,R) matrices. Their spectral properties allow a…
Quantum Teichmuller theory assigns invariants to three-manifolds via projective representations of mapping class groups derived from the representation of a noncommutative torus. Here, we focus on a representation of the simplest…
We construct a class of topological excitations of a mean field in a two-dimensional spin system represented by a quantum Heisenberg model with high powers of exchange interaction. The quantum model is associated with a classical one (the…
We discuss some properties of the tower of mapping class group representations associated to a Rational Conformal Field Theory. In particular, after reviewing the elementary properties of the modular representation, we discuss the Galois…
Let M be a one-holed torus with boundary $\partial M$ (a circle) and $\Gamma$ the mapping class group of M fixing $\partial M$. The group $\Gamma$ acts on ${\mathcal M}_{\mathcal C}(SU(2))$ which is the space of SU(2)-gauge equivalence…
Suppose we are given a profinite group $G$ acting on a formal moduli stack $\mathcal{M}$, and we want to understand the group action, and compute cohomology related to this group action. How can we do it? This prolegomenon surveys two…
After deriving the classical Ward identity for the variation of the action under a change of the modulus of the torus we map the problem of the sphere with four sources to the torus. We extend the method previously developed for computing…