Related papers: Chern Simons invariants in $KK$ theory
Let $M$ be a 3-manifold with a finite set $X(M)$ of conjugacy classes of representations $\rho:\pi_1(M)\to$SU$_2$. We study here the distribution of the values of the Chern-Simons function CS$:X(M)\to \mathbb{R}/2\pi\mathbb{Z}$. We observe…
We construct the functional integral of Abelian Chern-Simons theory with toral gauge group $\mathbb T=\mathfrak t/\Lambda \cong U(1)^n$ at level $K$, where $K:\Lambda\times\Lambda\to\mathbb Z$ is an even, integral, nondegenerate symmetric…
We give a precise definition and produce a path-integral computation of the normalized partition function of the abelian U(1) Chern-Simons field theory defined in a general closed oriented 3-manifold. We use the Deligne-Beilinson formalism,…
To each algebra over the complex numbers we associate a sequence of abelian groups in a contravariant functorial way. In degree (m-1) we have the m-summable Fredholm modules over the algebra modulo stable m-summable perturbations. These new…
The Fourier coefficients of a smooth $K$-invariant function on a compact symmetric space $M=U/K$ are given by integration of the function against the spherical functions. For functions with support in a neighborhood of the origin, we…
The aim of this note is to define for any $e_n$-algebra $A$ and a compact parallelizable n-manifold $M$ without borders a morphism from the homology of homotopy Lie algebra $A[n-1]$ to the topological chiral homology of $M$ with…
We formulate a refinement of SU(N) Chern-Simons theory on a three-manifold via the refined topological string and the (2,0) theory on N M5 branes. The refined Chern-Simons theory is defined on any three-manifold with a semi-free circle…
We introduce a new family of invariants of real algebraic sets defined in terms of the topology of their complexifications and compute some of these invariants for spheres. This allows us to completely classify topological isomorphism…
Chern-Simons (CS) invariant is a fundamental topological invariant describing the topological invariance of 3D space based on the Chern-Simons field theory. To date, direct measurement of the CS invariant in a physical system remains…
Quantum knot invariants (like colored HOMFLY-PT or Kauffman polynomials) are a distinguished class of non-perturbative topological invariants. Any known way to construct them (via Chern-Simons theory or quantum R-matrix) starts with a…
We obtain the Plancherel theorem for the quotient of a simple Lie group of real rank one by a convex-cocompact discrete subgroup and its consequences for the spectrum of locally invariant differential operators on bundles over Kleinian…
For three classes of elliptic pseudodifferential operators on a compact manifold with boundary which have `geometric K-theory', namely the `transmission algebra' introduced by Boutet de Monvel, the `zero algebra' introduced by Mazzeo and…
We define the notion of invariant derivation of a C*-algebra under a compact quantum group action and prove that in certain conditions, such derivations are generators of one parameter automorphism groups.
Polynomial invariants corresponding to the fundamental representation of the gauge group $SO(N)$ are computed for arbitrary torus knots in the framework of Chern-Simons gauge theory making use of knot operators. As a result, a formula which…
We construct an analytic multiplicative model of smooth K-theory. We further introduce the notion of a smooth K-orientation of a proper submersion and define the associated push-forward which satisfies functoriality, compatibility with…
The defect $d(M,\rho)$ is an invariant of a compact oriented 3-manifold $M$ with a representation $\rho$ of the fundamental group. In this article we give a diagrammatic method for $d$ of knot exteriors by using knot diagrams.
We present an explicit expression for the topological invariants associated to $SU(2)$ monopoles in the fundamental representation on spin four-manifolds. The computation of these invariants is based on the analysis of their corresponding…
On a polarized compact symplectic manifold endowed with an action of a compact Lie group, in analogy with geometric invariant theory, one can define the space of invariant functions of degree k. A central statement in symplectic geometry,…
We give a direct interpretation of Neumann's combinatorial formula for the Chern-Simons invariant of a 3-manifold with a representation in PSL(2,C) whose restriction to the boundary takes values in upper triangular matrices. Our…
A survey of some results and open questions related to the following algebraic invariants of compact complex manifolds, that can be obtained from differential forms: cohomology groups, Chern classes, rational homotopy groups, and higher…