Related papers: An index theorem in differential K-theory

For equivariant stable homotopy theory, equivariant KK-theory and equivariant derived categories, we show how restriction to a subgroup of finite index yields a finite commutative separable extension, analogous to finite \'etale extensions…

In this short paper, for any holomorphic submersion $\pi: X\rightarrow B$, we derive a criterion for $X$ to have K\"{a}hler structures. This criterion generalizes Blanchard's criterion for a special class of isotrivial holomorphic…

An isomorphism between two hermitian unitals is proved, and used to treat isomorphisms of classical groups that are related to the isomorphism between certain simple real Lie algebras of types A and D (and rank 3).

There is an equivalence relation on the set of smooth maps of a manifold into the stable unitary group, defined using a Chern-Simons type form, whose equivalence classes form an abelian group under ordinary block sum of matrices. This…

Boundary groupoids were introduced by the second author, which can be used to model many analysis problems on singular spaces. In order to investigate index theory on boundary groupoids, we introduce the notion of {\em a deformation from…

In geometric representation theory, it is common to compute equivariant $K$ theory of schemes like $Hilb^n ( \mathbb{A}^2 )$ or $Hilb^n (X)$ for an ALE resolution $X \to \mathbb{A}^2 / \Gamma$. If we abandon the algebraic nature and just…

We provide a proof in the language of model categories and symmetric spectra of Lurie's theorem that topological complex $K$-theory represents orientations of the derived multiplicative group. Then we generalize this result to the motivic…

Computational Group Theory is applied to indexed objects (tensors, spinors, and so on) with dummy indices. There are two groups to consider: one describes the intrinsic symmetries of the object and the other describes the interchange of…

In this note we give a simple, model-independent construction of Chern classes as natural transformations from differential complex K-theory to differential integral cohomology. We verify the expected behaviour of these Chern classes with…

The main theorem in this paper is that the base change functor from an abelian category $\cA$ to its polynomial category in the sense of Schlichting $-\otimes_{\cA}\bbZ[t]:\cA \to \cA[t]$ induces an isomorphism on their $K$-theories if…

In joint work with M. Hopkins and C. Teleman we find a new description of the Verlinde algebra associated to a compact Lie group. In this expository account we describe twisted K-theory, prove the theorem for the group SU(2), and motivate…

We prove the topological analogue of the period-index conjecture in each dimension away from a small set of primes.

We prove that if two conformal embeddings between Riemann surfaces with finite topology are homotopic, then they are isotopic through conformal embeddings. Furthermore, we show that the space of all conformal embeddings in a given homotopy…

We establish an integration theory for singular subalgebroids, by diffeological groupoids. To do so, we single out a class of diffeological groupoids satisfying specific properties, and we introduce a differentiation-integration procedure…

We study algebraic varieties parametrized by topological spaces and enlarge the domains of Lawson homology and morphic cohomology to this category. We prove a Lawson suspension theorem and splitting theorem. A version of Friedlander-Lawson…

We introduce and solve a period-index problem for the Brauer group of a topological space. The period-index problem is to relate the order of a class in the Brauer group to the degrees of Azumaya algebras representing it. For any space of…

We use correspondences to define a purely topological equivariant bivariant K-theory for spaces with a proper groupoid action. Our notion of correspondence differs slightly from that of Connes and Skandalis. We replace smooth K-oriented…

In this note we give equivalence of the existence of K-partitions with the existence of the precipitous ideal which is essentially topological. This way we strengthen the main result of Frankiewczi and Kunen (1987).

In a previous paper we have introduced the gauge-equivariant K-theory group of a bundle endowed with a continuous action of a bundle of compact Lie groups. These groups are the natural range for the analytic index of a family of…

Given a connected and locally compact Hausdorff space X with a good base K we assign, in a functorial way, a C(X)-algebra to any precosheaf of C*-algebras A defined over K. Afterwards we consider the representation theory and the Kasparov…