Related papers: Loop Differential K-theory

The caloron correspondence can be understood as an equivalence of categories between $G$-bundles over circle bundles and $LG \rtimes_\rho S^1$-bundles where $LG$ is the group of smooth loops in $G$. We use it, and lifting bundle gerbes, to…

Let $G$ be an affine group scheme over a noetherian commutative ring $R$. We show that every $G$-equivariant vector bundle on an affine toric scheme over $R$ with $G$-action is extended from $\Spec(R)$ for several cases of $R$ and $G$. We…

Let $R$ be a ring spectrum and $ E\to X$ an $R$-module bundle of rank $n$. Our main result is to identify the homotopy type of the group-like monoid of homotopy automorphisms of this bundle, $hAut^R(E)$. This will generalize the result…

We describe a map from the equivariant twisted K-homology of a compact, connected, simply connected Lie group $G$ to the Verlinde ring. Our map is described at the level of `D-cycles' for the geometric twisted K-homology of $G$, and is…

In this paper we study the "holomorphic K-theory" of a projective variety, which is defined in terms of the homotopy type of spaces of holomorphic maps from the variety to Grassmannians and loop groups. This theory was introduced by Lawson,…

We prove a twisting theorem for nodal classes in permutation-equivariant quantum $K$-theory, and combine it with existing theorems of Givental to obtain a twisting result for general characteristic classes of the virtual tangent bundle.…

In this paper we define twisted equivariant K-theory for actions of Lie groupoids. For a Bredon-compatible Lie groupoid, this defines a periodic cohomology theory on the category of finite CW-complexes with equivariant stable projective…

We compute the convolution product on the equivariant K-groups of the cyclic quiver variety. We get a q-analogue of double-loop algebras, closely related to the toroidal quantum groups previously studied by the authors. We also give a…

We show that if two rings have equivalent derived categories then they have the same algebraic K-theory. Similar results are given for G-theory, and for a large class of abelian categories.

We extend the notion of a spectral triple to that of a higher-order relative spectral triple, which accommodates several types of hypoelliptic differential operators on manifolds with boundary. The bounded transform of a higher-order…

We interpret certain equivariant Kasparov groups as equivariant representable K-theory groups. We compute these groups via a classifying space and as K-theory groups of suitable sigma-C*-algebras. We also relate equivariant vector bundles…

The proper action functional of (4k+3)-dimensional U(1)-Chern-Simons theory including the instanton sectors has a well known description: it is given on the moduli space of fields by the fiber integration of the cup product square of…

A group action on the input ring or category induces an action on the algebraic $K$-theory spectrum. However, a shortcoming of this naive approach to equivariant algebraic $K$-theory is, for example, that the map of spectra with $G$-action…

In this article we describe the $T_{comp}$-equivariant topological $K$-ring of a $T$-{\it cellular} complete toric variety. We further show that $K_{T_{comp}}^0(X)$ is isomorphic as an $R(T_{comp})$-algebra to the ring of piecewise Laurent…

We reformulate the construction of Kontsevich's completion and use Lawson homology to define many new motivic invariants. We show that the dimensions of subspaces generated by algebraic cycles of the cohomology groups of two $K$-equivalent…

A new approach to the quantization of Chern-Simons theory has been developed in recent papers of the author. It uses a "simulation" of the moduli space of flat connections modulo the gauge group which reveals to be related to a lattice…

We compute the equivariant $K$-theory $K_G^*(G)$ for a simply connected Lie group $G$ (acting on itself by conjugation). We prove that $K_G^*(G)$ is isomorphic to the algebra of Grothendieck differentials on the representation ring. We also…

We construct and study a new topological field theory in three dimensions. It is a hybrid between Chern-Simons and Rozansky-Witten theory and can be regarded as a topologically-twisted version of the N=4 d=3 supersymmetric gauge theory…

This paper is part of a sequence interpreting quantities of conformal field theories K-theoretically. Here we give geometric constructions of the associated module categories (modular invariants, nimreps, etc). In particular, we give a…

Recent discoveries make it possible to compute the K-theory of certain rings from their cyclic homology and certain versions of their cdh-cohomology. We extend the work of G. Corti\~nas et al. who calculated the K-theory of, in addition to…