Related papers: BRS-Chern-Simons forms and cyclic homology
We consider a biparametric family of BRS invariant regularization methods of SU(N) Chern-Simons theory (the parameters defining the family taking arbitrary values in $\RR^2$) and show that the shift $k\to k + sign(k) N$ of the Chern-Simons…
These lecture notes contain an exposition of basic ideas of K-theory and cyclic cohomology. I begin with a list of examples of various situations in which the K-functor of Grothendieck appears naturally, including the rudiments of the…
In this paper we compute the K-theory (algebraic and topological) and entire periodic cyclic homology for compact quantum groups, define Chern characters between them and show that the Chern characters in both topological and algebraic…
We analyze the relationship between Bott periodicity in topological $K$-theory and the natural periodicity of cyclic homology. This is a basis for understanding the multiplicativity, in odd dimensions, of a bivariant Chern-Connes character…
We show a quantum version of Chern character homomorphism from the small quantum K-theory to the small quantum cohomology in the cases of projective spaces and incidence varieties, whose classical limit gives the classical Chern character…
A method to obtain explicit and complete topological solution of SU(2) Chern-Simons theory on $S^3$ is developed. To this effect the necessary aspects of the theory of coloured-oriented braids and duality properties of conformal blocks for…
We introduce Chern classes in $U(m)$-equivariant homotopical bordism that refine the Conner-Floyd-Chern classes in the $MU$-cohomology of $B U(m)$. For products of unitary groups, our Chern classes form regular sequences that generate the…
We construct a Baum-Douglas type model for $K$-homology with coefficients in $\mathbb{Z}/k\mathbb{Z}$. The basic geometric object in a cycle is a $spin^c$ $\mathbb{Z}/k\mathbb{Z}$-manifold. The relationship between these cycles and the…
We discuss $w_\infty$ and $sl_q(2)$ symmetries in multiple Chern-Simons theory on a torus. It is shown that these algebraic structures arise from the dynamics of the non-integrable phases of the Chern-Simons fields. The generators of these…
We study the Bott-Chern cohomology of complex orbifolds obtained as quotient of a compact complex manifold by a finite group of biholomorphisms.
We compute the Chern-Simons transgressed forms of some modularly invariant characteristic forms, which are related to the elliptic genera. We study the modularity properties of these secondary characteristic forms and the relations among…
We give an algorithm for computing the contact homology of some Brieskorn manifolds. As an application, we construct infinitely many contact structures on the class of simply connected contact manifolds that admit nice contact forms (i.e.…
We give a Dehn-Nielsen type theorem for the homology cobordism group of homology cylinders by considering its action on the acyclic closure, which was defined by Levine, of a free group. Then we construct an additive invariant of those…
We present an approach to cyclic homology of A_{\infty} algebras. Our main technical tool is the concept of X-complex due to Cuntz and Quillen. This, in particular, enables us to compute the periodic cyclic homology of an A_{\infty} algebra…
We present a geometric approach, in the spirit of the Chern-Weil theory, for constructing cocycles representing the classes of the Hopf cyclic cohomology of the Hopf algebra H(n) relative to GL(n, R). This provides an explicit description…
We construct a Chern character map from the K-theory of the reduced C^* algebra of the p-adic GL(n) with values in the periodic cyclic homology of the Schwartz algebra of this group. We prove that this map is an isomorphism after tensoring…
In this paper we introduce a common framework for describing the topological part of the Baum-Connes conjecture for a wide class of groups. We compute the Bredon homology for groups with aspherical presentation, one-relator quotients of…
Graphs with given k vertices generate an (acyclic) simplicial complex. We describe the homology of its quotient complex, formed by all connected graphs, and demonstrate its applications to the topology of braid groups, knot theory,…
In this paper we complete the classification of topological symmetry groups for complete graphs $K_n$ by characterizing which $K_n$ can have a cyclic group, a dihedral group, or a subgroup of $D_m \times D_m$ where $m$ is odd, as its…
We introduce and study elementary properties of graph homology of algebras. This new homology theory shares many features of cyclic and Hochschild homology. We also define a graph K-theory together with an analog of Chern character.