Related papers: An index theorem in differential K-theory

By analogy with algebraic geometry, we define a category of non-linear sheaves (quasi-coherent homotopy-sheaves of topological spaces) on projective toric varieties and prove a splitting result for its algebraic K-theory, generalising…

These are some notes on the basic properties of algebraic K-theory and G-theory of derived algebraic spaces and stacks, and the theory of fundamental classes in this setting.

Cheeger-Simons differential characters and differential $K$-theory are refinements of ordinary cohomology theory and topological $K$-theory respectively, and they are examples of differential cohomology. Each of these differential…

Let $A$ be a graded C*-algebra. We characterize Kasparov's K-theory group $\hat{K}_0(A)$ in terms of graded *-homomorphisms by proving a general converse to the functional calculus theorem for self-adjoint regular operators on graded…

We investigate the properties of relative analogues of admissible Ind, Pro, and elementary Tate objects for pairs of exact categories, and give criteria for those categories to be abelian. A relative index map is introduced, and as an…

Given $\varepsilon_0>0$, $I\in \mathbb{N}\cup \{0\}$ and $K_0,H_0\geq0$, let $X$ be a complete Riemannian $3$-manifold with injectivity radius $\mbox{Inj}(X)\geq \varepsilon_0$ and with the supremum of absolute sectional curvature at most…

Let $M$ be a $n$-dimensional complex manifold and $f,g:M\to M$ two distinct holomorphic self-maps. Suppose that $f$ and $g$ coincide on a globally irreducible compact hypersurface $S\subset M$. We show that if one of the two maps is a local…

This paper deals with the construction of a suitable topological $K$-theory capable of classifying topological phases of dynamically stable systems described by gapped $\eta$-self-adjoint operators on a Krein space with indefinite metric…

We prove a non-linear version of a theorem of Grayson which is an analogue of the Fundamental Theorem of Algebraic $K$-theory and identify the $K$-theory of the endomorphism category over a space $X$ in terms of reduced $K$-theory of a…

We build on work of Kellendonk, Richard, Tiedra de Aldecoa and others to show that the wave operators for Schr\"{o}dinger scattering theory on $\mathbb{R}^n$ generically have a particular form. As a consequence, Levinson's theorem can be…

We investigate, using purely combinatorial methods, structural and algorithmic properties of linear equivalence classes of divisors on tropical curves. In particular, an elementary proof of the Riemann-Roch theorem for tropical curves,…

This is an expository account of the following result: we can construct a group by means of twisted Z_2-graded vectorial bundles which is isomorphic to K-theory twisted by any degree three integral cohomology class.

A differential-algebraic approach to studying the Lax type integrability of the generalized Riemann type hydrodynamic hierarchy is revisited, its new Lax type representation and Poisson structures constructed in exact form. The related…

In previous papers (arxiv:math/0612370 and arxiv:0909.1342) we defined the C*-algebra and the longitudinal pseudodifferential calculus of any singular foliation (M,F). Here we construct the analytic index of an elliptic operator as a…

Let $X$ be a toric $\mbox{hyperK\"ahler}$ manifold. The purpose of this note is to describe the topological $K$-ring $K^*(X)$ of $X$. We give a presentation for the topological $K$-ring in terms of generators and relations similar to the…

Recall that the definition of the $K$-theory of an object C (e.g., a ring or a space) has the following pattern. One first associates to the object C a category A_C that has a suitable structure (exact, Waldhausen, symmetric monoidal, ...).…

The paper is devoted to the discussion of index theorem for domain walls condition. We give an extension of the theorem to the case, when not only Yang-Mills connection components have a jump on some surface of co-dimension 1, but also…

We show that the classification of the symmetric spaces can be achieved by K-theoretical methods. We focus on Hermitian symmetric spaces of non-compact type, and define K-theory for JB*-triples along the lines of C*-theory. K-groups have to…

Starting from its original definition in module categories with respect to projective modules, the index has played an important role in various aspects of homological algebra, categorification of cluster algebras and $K$-theory. In the…

We prove an index theorem for families of linear periodic Hamiltonian systems, which is reminiscent of the Atiyah-Singer index theorem for selfadjoint elliptic operators. For the special case of one-parameter families, we compare our…