相关论文: Extended Bloch group and the Chern-Simons class (I…
We discuss the N=2 supersymmetric extension of the gauged O(3) sigma model in (2+1) dimensions with an abelian Chern-Simons term. It is shown that the self-dual potential and the Bogomolny relations naturally appear as consequences of…
We prove the existence of positive lower bounds on the Cheeger constants of manifolds of the form $X/\Gamma$ where $X$ is a contractible Riemannian manifold and $\Gamma<\Isom(X)$ is a discrete subgroup, typically with infinite co-volume.…
This paper is an expansion of my lecture for David Epstein's birthday, which traced a logical progression from ideas of Euclid on subdividing polygons to some recent research on invariants of hyperbolic 3-manifolds. This `logical…
In this paper we consider the cohomology of a closed arithmetic hyperbolic 3-manifold with coefficients in the local system defined by the even symmetric powers of the standard representation of SL(2,C). The cohomology is defined over the…
We give a definition of differentiable cohomology of a Lie group G (possibly infinite-dimensional) with coefficients in any abelian Lie group. This differentiable cohomology maps both to the cohomology of the group made discrete and to Lie…
Building on Hitchin's work of the Wess-Zumino-Witten term for harmonic maps into Lie groups, we derive a formula for the enclosed volume of a compact CMC surface $f$ in $\mathbb S^3$ in terms of a holonomy on the Chern-Simons bundle and the…
We construct a new class of topological surface defects in Chern-Simons theory with non-compact, non-Abelian gauge groups. These defects are characterized by isotropic subalgebras defined by solutions of the modified classical Yang-Baxter…
The purpose of this paper is to extend our previous work on the variational formula for the Bismut-Cheeger eta form without the kernel bundle assumption by allowing the spin$^c$ Dirac operators to be twisted by isomorphic vector bundles,…
We consider several generalizations of the classical $\gamma$-positivity of Eulerian polynomials (and their derangement analogues) using generating functions and combinatorial theory of continued fractions. For the symmetric group, we prove…
An explicit formula for the Schur multiplier of the group of unitriangular matrices over products of cyclic rings $\ZZ/m\ZZ$ and $\ZZ$ is derived. We use it to provide presentations of the corresponding covering groups and touch upon the…
We show how to make the additive Chow groups of Bloch-Esnault, Ruelling and Park into a graded module for Bloch's higher Chow groups, in the case of a smooth projective variety over a field. This yields a a projective bundle formula as well…
This note is an application of classification results for finite-dimensional Nichols algebras over groups. We apply these results to generalizations of Fomin--Kirillov algebras to complex reflection groups. First, we focus on the case of…
We present a general method for the computation of tree-level superpotentials for the world-volume theory of B-type D-branes. This includes quiver gauge theories in the case that the D-brane is marginally stable. The technique involves…
In the paper [1] (arXiv:math/0408333) the authors discuss two possible definitions of the relative Cheeger-Simons characters, the second one fitting into a long exact sequence. Here we relate that picture to the one of the relative Deligne…
We prove quite general statements about functional equations in any number of variables for the dilogarithms defined by Bloch-Wigner, Rogers, and Coleman, showing that they follow from certain 5-term and 2-term relations in a precise way.…
Recently, Gekeler proved that the group of invertible analytic functions modulo constant functions on Drinfeld's upper half space is isomorphic to the dual of an integral generalized Steinberg representation. In this note we show that the…
We give a general method for computing the cyclic cohomology of crossed products by etale groupoids, extending the Feigin-Tsygan-Nistor spectral sequences. In particular we extend the computations performed by Brylinski, Burghelea,Connes…
After recalling the precise existence conditions of the zeta function of a pseudodifferential operator, and the concept of reflection formula, an exponentially convergent expression for the analytic continuation of a multidimensional…
Aganagic and Shakirov propose a refinement of the SU(N) Chern-Simons theory for links in three manifolds with S^1-symmetry, such as torus knots in S^3, based on deformation of the S and T matrices, originally found by Kirillov and…
We develop methods for constructing explicit generators, modulo torsion, of the K_3-groups of imaginary quadratic number fields. These methods are based on either tessellations of hyperbolic 3-space or on direct calculations in suitable…