Related papers: Almost commuting elements in compact Lie groups

In this paper we analyse the topological group cohomology of finite-dimensional Lie groups. We introduce a technique for computing it (as abelian groups) for torus coefficients by the naturally associated long exact sequence. The upshot in…

Recently we suggested a new quantum algebra, the moduli algebra, which was conjectured to be a quantum algebra of observables of the Hamiltonian Chern Simons theory. This algebra provides the quantization of the algebra of functions on the…

We consider the moduli space of flat G-bundles over the twodimensional torus, where G is a real, compact, simple Lie group which is not simply connected. We show that the connected components that describe topologically non-trivial bundles…

Homogeneous compatible almost complex structures on symplectic manifolds are studied, focusing on those which are special, meaning that their Chern-Ricci form is a multiple of the symplectic form. Non Chern-Ricci flat ones are proven to be…

% A new, formal, non-combinatorial approach to invariants of % three-dimensional manifolds of Reshetikhin, Turaev and % Witten in the framework of non-perturbative topological % quantum Chern-Simons theory, corresponding to an arbitrary %…

We introduce a notion of deformations of quasi-Hamiltonian $G$-spaces to Hamiltonian $G$-spaces and provide several examples. In particular, we show that the double $G \times G$ of a Lie group, viewed as a quasi-Hamiltonian $G \times…

There exists a large class of groups of operators acting on Hilbert spaces, where commutativity of group elements can be expressed in the geometric language of symplectic polar spaces embedded in the projective spaces PG($n, p$), $n$ being…

We develop the theory of Chern-Simons bundle 2-gerbes and multiplicative bundle gerbes associated to any principal $G$-bundle with connection and a class in $H^4(BG, \ZZ)$ for a compact semi-simple Lie group $G$. The Chern-Simons bundle…

We make cohomological computations related to the moduli space of genus three curves with symplectic level two structure by means of counting points over finite fields. In particular, we determine the cohomology groups of the quartic locus…

In this note, we give a description of the modular functor associated to the Chern-Simons theory with a finite group from the complex-analytic point of view, i.e. as a vector bundle with a flat connection on the moduli space of punctured…

We compute cohomology of the moduli space of genus three curves with level two structure and some related spaces. In particular, we determine the cohomology groups of the moduli space of plane quartics with level two structure as…

The moduli spaces for Higgs bundles associated to real Lie groups and a closed Riemann surface have multiple connected components. This survey provides a compendium of results concerning the counting of these components in cases where the…

In this paper we discuss decomposition in the context of three-dimensional Chern-Simons theories. Specifically, we argue that a Chern-Simons theory with a gauged noneffectively-acting one-form symmetry is equivalent to a disjoint union of…

We prove that, for any n, there are simply-connected four-manifolds which admit n-tuples of symplectic forms whose first Chern classes have pairwise different divisibilities in integral cohomology. It follows that the moduli space of…

We study the moduli space $\fM^s(6;3,6,4)$ of simple rank 6 vector bundles $\E$ on $\PP^3$ with Chern polynomial $1+3t+6t^2+4t^3$ and properties of these bundles, especially we prove some partial results concerning their stability. We first…

We study the almost Kaehler geometry of adjoint orbits of non-compact real semisimple Lie groups endowed with the Kirillov-Kostant-Souriau symplectic form and a canonically defined almost complex structure. We give explicit formulas for the…

The paper contains three main results. First, we show that if a commutative semigroup variety is a modular element of the lattice Com of all commutative semigroup varieties then it is either the variety COM of all commutative semigroups or…

For any almost-simple group $G$ over an algebraically closed field $k$ of characteristic zero, we describe the automorphism group of the moduli space of semistable $G$-bundles over a connected smooth projective curve $C$ of genus at least…

In this note we study topological invariants of the spaces of homomorphisms Hom(\pi,G), where \pi\ is a finitely generated abelian group and G is a compact Lie group arising as an arbitrary finite product of the classical groups SU(r), U(q)…

We classify Lie 3-algebras possessing an invariant lorentzian inner product. The indecomposable objects are in one-to-one correspondence with compact real forms of metric semisimple Lie algebras. We analyse the moduli space of classical…