Related papers: Regulators and cycle maps in higher-dimensional di…

We derive formulas and algorithms for Kitaev's invariants in the periodic table for topological insulators and superconductors for finite disordered systems on lattices with boundaries. We find that K-theory arises as an obstruction to…

A general specialization map is constructed for higher Chow groups and used to prove a "going-up" theorem for algebraic cycles and their regulators. The results are applied to study the degeneration of the modified diagonal cycle of Gross…

For a ring $R$, we construct a universal $K_R$-torsor $\mathcal{T}_R\to K_{Tate(R)}$ on the $K$-theory space of Tate $R$-modules. This torsor is closely related to canonical central extensions of loop groups. Just like classical loop group…

This paper describes the $K$-theory structure for three algebra classes. For cyclic $p$-group rings and truncated polynomial rings over $\mathbb{Z}/p^s\mathbb{Z}$, we determine reduced $K_2$-structures via a common algebraic framework. For…

We introduce a version of algebraic $K$-theory for coefficient systems of rings which is valued in genuine $G$-spectra for a finite group $G$. We use this construction to build a genuine $G$-spectrum $K_G(\mathbb{Z}[\underline{\pi_1(X)}])$…

We construct a model of differential K-theory, using the geometrically defined Chern forms, whose cocycles are certain equivalence classes of maps into the Grassmannians and unitary groups. In particular, we produce the circle-integration…

Borel's construction of the regulator gives an injective map from the algebraic $K$-groups of a number field to its Deligne-Beilinson cohomology groups. This has many interesting arithmetic and geometric consequences. The formula for the…

A equivalence relation, preserving the Chern-Weil form, is defined between connections on a complex vector bundle. Bundles equipped with such an equivalence class are called Structured Bundles, and their isomorphism classes form an abelian…

We compare the deformation theory and the analytic structure of the Seiberg-Witten moduli spaces of a K\"ahler surface to the corresponding components of the Hilbert scheme, and show that they are isomorphic. Next we show how to compute the…

A kind of motivic algebra of spectral categories and modules over them is developed to introduce K-motives of algebraic varieties. As an application, bivariant algebraic K-theory as well as bivariant motivic kohomology groups are defined…

The Chern classes of a K-theory class which is represented by a vector bundle with connection admit refinements to Cheeger-Simons classes in Deligne cohomology. In the present paper we consider similar refinements in the case where the…

We construct Adams operations on the rational higher arithmetic K-groups of a proper arithmetic variety. The definition applies to the higher arithmetic K-groups given by Takeda as well as to the groups suggested by Deligne and Soule, by…

Regular algebraic $K$-theory for groups is a homology theory for discrete groups closely connected (but different from) group homology. It also gives a version of algebraic $K$-theory for rings by the simple functorial mapping assigning to…

We give an infinite dimensional description of the differential K-theory of a manifold $M$. The generators are triples $[H, A, \omega]$ where $H$ is a ${\bf Z}_2$-graded Hilbert bundle on $M$, $A$ is a superconnection on $H$ and $\omega$ is…

We construct classes in the motivic cohomology of certain 1-parameter families of Calabi-Yau hypersurfaces in toric Fano n-folds, with applications to local mirror symmetry (growth of genus 0 instanton numbers) and inhomogeneous…

This is a companion to a recent investigation of K-theoretical invariants for symmetric spaces. We introduce a new class of cycles in K-groups, which are connected to elements of an underlying root lattice. This will be needed for a…

I conjecture that index formulas for $K$-theory classes on the moduli of holomorphic $G$-bundles over a compact Riemann surface $\Sigma$ are controlled, in a precise way, by Frobenius algebra deformations of the Verlinde algebra of $G$. The…

Let $k$ be an algebraically closed field and $\alpha$, $\beta$, $\gamma$ be partitions. An algebraic group acts on the constructible set of short exact sequences of nilpotent $k$-linear operators of Jordan types $\alpha$, $\beta$, and…

A numerical scheme is developed for solution of the Goursat problem for a class of nonlinear hyperbolic systems with an arbitrary number of independent variables. Convergence results are proved for this difference scheme. These results are…

In this paper we study the group K_{2n}^{(n+1)}(F) where F is the function field of a complete, smooth, geometrically irreducible curve C over a number field, assuming the Beilinson--Soul\'e conjecture on weights. In particular, we compute…