Related papers: Differential K-theory. A survey

Let $R$ be the homogeneous coordinate ring of a smooth projective variety $X$ over a field $\k$ of characteristic~0. We calculate the $K$-theory of $R$ in terms of the geometry of the projective embedding of $X$. In particular, if $X$ is a…

We introduce two $K$-theories, one for vector bundles whose fibers are modules of vertex operator algebras, another for vector bundles whose fibers are modules of associative algebras. We verify the cohomological properties of these…

In this paper it is shown that multiplicative cohomology theories that are rationally even -- a technical condition that is often satisfied -- the Hopkins-Singer construction of generalized differential cohomology has a unital, graded…

We construct the Atiyah-Hirzebruch spectral sequence (AHSS) for twisted differential generalized cohomology theories. This generalizes to the twisted setting the authors' corresponding earlier construction for differential cohomology…

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…

Let G be a compact connected Lie group, and (M,\omega) a Hamiltonian G-space with proper moment map \mu. We give a surjectivity result which expresses the K-theory of the symplectic quotient M//G in terms of the equivariant K-theory of the…

Generalizing differential geometry of smooth vector bundles formulated in algebraic terms of the ring of smooth functions, its derivations and the Koszul connection, one can define differential operators, differential calculus and…

The kinematical part of general theory of deformational structures on smooth manifolds is developed. We introduce general concept of d-objects deformation, then within the set of all such deformations we develop some special algebra and…

We describe a symmetry breaking construction in coarse geometry which allows to obtain information about equivariant coarse homology classes by restriction to smaller groups and spaces. In the case of equivariant coarse $K$-homology theory…

We compute the equivariant complex K-theory ring of a cohomogeneity-one action of a compact Lie group at the level of generators and relations and derive a characterization of K-theoretic equivariant formality for these actions. Less…

Let X --> B be a proper submersion with a Riemannian structure. Given a differential K-theory class on X, we define its analytic and topological indices as differential K-theory classes on B. We prove that the two indices are the same.

In this expository article, we outline the theory of harmonic differential forms and its consequences. We provide self-contained proofs of the following important results in differential geometry: (1) Hodge theorem, which states that for a…

Dynamical quantum field theories (QFTs), such as those in which spacetimes are equipped with a metric and/or a field in the form of a smooth map to a target manifold, can be formulated axiomatically using the language of…

We establish a connection between continuous K-theory and integral cohomology of rigid spaces. Given a rigid analytic space over a complete discretely valued field, its continuous K-groups vanish in degrees below the negative of the…

In this note we prove some results in flat and differential $K$-theory. The first one is a proof of the compatibility of the differential topological index and the flat topological index by a direct computation. The second one is the…

Given an ample groupoid, we construct a spectral sequence with groupoid homology with integer coefficients on the second sheet, converging to the K-groups of the (reduced) groupoid C*-algebra, provided the groupoid has torsion-free…

We show that the Atiyah-Hirzebruch K-theory of spaces admits a canonical generalization for stratified spaces. For this we study algebraic constructions on stratified vector bundles. In particular the tangent bundle of a stratified manifold…

We define a group of relative differential K-characters associated with a smooth map between two smooth compact manifolds. We show that this group fits into a short exact sequence as in the non-relative case. Some secondary geometric…

We define secondary theories and characteristic classes for simplicial smooth manifolds generalizing Karoubi's multiplicative K-theory and multiplicative cohomology groups for smooth manifolds. As a special case we get versions of the…

This note gives an overview of the mathematical framework underlying topological insulators, highlighting the connection to K-theory and vector bundles. We see ``real'' and ``quaternionic'' vector bundles arise naturally in the presence of…