相关论文: $K$-theory of $\mbox{hyperK\"ahler}$ toric manifol…
We describe the $K$-ring of a quasi-toric manifold in terms of generators and relations. We apply our results to describe the $K$-ring of Bott-Samelson varieties.
The aim of this paper is to describe the topological $K$-ring, in terms of generators and relations of a flag Bott manifold. We apply our results to give a presentation for the topological K-ring and hence the Grothendieck ring of algebraic…
The aim of these notes is to acquaint the reader with important objects in complex algebraic geometry: K3 surfaces and their higher-dimensional analogs, hyperk\"ahler manifolds. These manifolds are interesting from several points of view:…
The {\it torus manifolds} have been defined and studied by M. Masuda and T. Panov (arXiv:math.AT/0306100) who in particular describe its cohomology ring structure. In this note we shall describe the topological $K$-ring of a class of torus…
The K-rings of non-singular complex pro jective varieties as well as quasi- toric manifolds were described in terms of generators and relations in an earlier work of the author with V. Uma. In this paper we obtain a similar description for…
In this article we describe the equivariant and ordinary topological $K$-ring of a toric bundle with fiber a $T$-{\it cellular} toric variety. This generalizes the results in \cite{su} on $K$-theory of smooth projective toric bundles. We…
Recent advances in computational techniques for $K$-theory allow us to describe the $K$-theory of toric varieties in terms of the $K$-theory of fields and simple cohomological data.
In this paper we provide descriptions of the Whitehead groups with coefficients in a ring of the Hilbert modular group and its reduced version, as well as for the topological K-theory of $C^*$-algebras, after tensoring with $\mathbb{Q}$, by…
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…
The Torelli group $\mathcal T(X)$ of a closed smooth manifold $X$ is the subgroup of the mapping class group $\pi_0(\mathrm{Diff}^+(X))$ consisting of elements which act trivially on the integral cohomology of $X$. In this note we give…
This work is devoted to the study of the foundations of quantum K-theory, a K-theoretic version of quantum cohomology theory. In particular, it gives a deformation of the ordinary K-ring K(X) of a smooth projective variety X, analogous to…
In this survey article we describe the geometry of toric hyperk\"ahler varieties, which are hyperk\"ahler quotients of the quaternionic vector spaces by tori. In particular, we discuss the Betti numbers, the cohomology ring, and variation…
Twisted complex $K$-theory can be defined for a space $X$ equipped with a bundle of complex projective spaces, or, equivalently, with a bundle of C$^*$-algebras. Up to equivalence, the twisting corresponds to an element of $H^3(X;\Z)$. We…
We present here the K-theoretic version of mirror models of toric manifold. First, we recall the construction of cohomological mirrors for toric manifolds, i.e. representations of the toric hypergeometric functions from quantum cohomology…
These are notes on twisted K-homology theory and twisted Ext-theory from the C*-algebra viewpoint, part of a series of talks on ``C*-algebras, noncommutative geometry and K-theory'', primarily for physicists.
We introduce a homology theory for k-graphs and explore its fundamental properties. We establish connections with algebraic topology by showing that the homology of a k-graph coincides with the homology of its topological realisation as…
We study twisted $Spin^c$-manifolds over a paracompact Hausdorff space $X$ with a twisting $\alpha: X \to K(\ZZ, 3)$. We introduce the topological index and the analytical index on the bordism group of $\alpha$-twisted $Spin^c$-manifolds…
We show how certain topological properties of co-K{\"a}hler manifolds derive from those of the K\"ahler manifolds which construct them. We go beyond Betti number results and describe the cohomology algebra structure of co-K\"ahler…
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 give an elementary introduction to hyperk\"ahler manifolds, survey some of their interesting properties and some open problems.