Related papers: A Geometric Model for Odd Differential K-theory

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.…

We define a Grassmann odd analogue of a Carrollian manifold as a supermanifold of dimension $n|1$ with an even degenerate metric such that the kernel is generated by a non-singular odd vector field that is a supersymmetry generator.…

Let V be a smooth variety defined over the real numbers. Every algebraic vector bundle on V induces a complex vector bundle on the underlying topological space V(C), and the involution coming from complex conjugation makes it a Real vector…

A version of smooth K-theory is constructed, which is adapted to the total Chern class instead of the Chern character (contrarily to previous theories). Some total Chern class morphism from this K-theory to Cheeger-Simons differential…

We investigate the generic 3D topological field theory within AKSZ-BV framework. We use the Batalin-Vilkovisky (BV) formalism to construct explicitly cocycles of the Lie algebra of formal Hamiltonian vector fields and we argue that the…

The purpose of this work is to give a definition of a topological K-theory for dg-categories over C and to prove that the Chern character map from algebraic K-theory to periodic cyclic homology descends naturally to this new invariant. This…

We introduce a parametrized version of scissors congruence $K$-theory of manifolds with tangential structure, which includes a topologized version of the scissors congruence $K$-theory of oriented manifolds as a special case. We examine the…

We give a precise formulation of T-duality for Ramond-Ramond fields. This gives a canonical isomorphism between the "geometrically invariant" subgroups of the twisted differential K-theory of certain principal torus bundles. Our result…

We construct a comparison map from the topological K-theory of the dg-category of twisted perfect complexes on certain global quotient stacks to twisted equivariant K-theory, generalizing constructions of Halpern-Leistner-Pomerleano and…

We describe the index pairing between an odd K-theory class and an odd unbounded Kasparov module by a pair of quasi-projections, supported on a submodule obtained from a finite spectral truncation. We achieve this by pairing the K-theory…

Gauge invariant topological interactions, such as the D=5 Chern-Simons terms, are required in models in extra dimensions that split anomaly free representations. The Chern-Simons term is necessary to maintain the overall anomaly…

In the present paper we propose a geometric model of the twisted K-theory corresponding to elements of finite order in $H^3(X, \mathbb{Z})\times [X, \BBSU_\otimes]$.

An equivariant Thom isomorphism theorem in operator K-theory is formulated and proven for infinite rank Euclidean vector bundles over finite dimensional Riemannian manifolds. The main ingredient in the argument is the construction of a…

In the example of complex grassmannians, we demonstrate various techniques available for computing genus-0 K-theoretic GW-invariants of flag manifolds and more general quiver varieties. In particular, we address explicit reconstruction of…

Let $M$ be a closed manifold and $\alpha : \pi_1(M)\to U_n$ a representation. We give a purely $K$-theoretic description of the associated element $[\alpha]$ in the $K$-theory of $M$ with $\R/\Z$-coefficients. To that end, it is convenient…

Complex Chern-Simons bundles are line bundles with connection, originating in the study of quantization of moduli spaces of flat connections with complex gauge groups. In this paper we introduce and study these bundles in the families…

To each second-order ordinary differential equation $\sigma $ on a smooth manifold $M$ a $G$-structure $P^\sigma $ on $J^1(\mathbb{R},M)$ is associated and the Chern connection $\nabla ^\sigma $ attached to $\sigma $ is proved to be…

In this paper we study the holomorphic Euler characteristics of determinant line bundles on moduli spaces of rank 2 semistable sheaves on an algebraic surface X, which can be viewed as $K$-theoretic versions of the Donaldson invariants. In…

We extend the Chern character on K-theory, in its generalization to the Chern-Dold character on generalized cohomology theories, further to (twisted, differential) non-abelian cohomology theories, where its target is a non-abelian de Rham…

Considering successive extensions of primary translationally shape invariant potentials, we enlarge the Krein-Adler theorem to mixed chains of state adding and state-deleting Darboux-B\"acklund transformations. It allows us to establish…