Related papers: Localization formulae in odd K-theory

We study K-theory classes of Hamiltonian loop group spaces represented by admissible Fredholm complexes. We prove various equivariant index formulae in this context. In a sequel to this article we show that, when specialized to a family of…

We define a cohomology for an arbitrary $K$-linear semistrict semigroupal 2-category $(\mathfrak{C},\otimes)$ (called in the paper a Gray semigroup) and show that its first order (unitary) deformations, up to the suitable notion of…

Let X be a pointed connected simplicial set with loop group G. The linearisation map in K-theory as defined by Waldhausen uses G-equivariant spaces. This paper gives an alternative description using presheaves of sets and abelian groups on…

This paper studies, for a positive integer $m$, the subalgebra of the cohomology ring of the complex Grassmannians generated by the elements of degree at most $m$. We build in two ways upon a conjecture for the Hilbert series of this…

For a root system R, a field K and a "choice of coefficients in K" we define a category of graded spaces with operators and study some of its properties. Then we assume that the coefficients are given by quantum binomials. We use basic…

We show how to compute a certain group of equivalence classes of invariant Drinfeld twists on the algebra of a finite group G over a field k of characteristic zero. This group is naturally isomorphic to the second lazy cohomology group of…

Local Hochschild, cyclic Homology and K-theory were introduced by N. Teleman in [10] with the purpose of unifying different settings of the index theorem. This paper is one of the research topics announced in [10], {\S}10. The definition of…

Given a connected manifold with corners of any codimension there is a very basic and computable homology theory called conormal homology defined in terms of faces and orientations of their conormal bundles, and whose cycles correspond…

This is a paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In three previous papers, we introduce the notion of formal manifolds and study…

In the present paper we describe the action of (not necessarily line) bundles of finite order on the $K$-functor in terms of classifying spaces. This description might provide with an approach for more general twistings in $K$-theory than…

Cohomological genus-0 Gromov-Witten invariants of a given target space can be encoded by the "descendant potential," a generating function defined on the space of power series in one variable with coefficients in the cohomology space of the…

Let G be a semisimple Lie group with no compact factors, K a maximal compact subgroup of G, and $\Gamma$ a lattice in G. We study automorphic forms for $\Gamma$ if G is of real rank one with some additional assumptions, using dynamical…

For a Fano manifold M, complex conjugation defines a real involution on the quantum cohomology ring. For the Grassmannian we identify this involution with an explicit transformation on Schubert classes defined over the integers. It is a…

We use Bott-Samelson resolutions of Schubert varieties in Grassmannians along with equiariant localization techniques to show that the factorial Schur functions and the factorial Grothendieck polynomials represent Schubert classes in…

By using K-theory, we construct a map from the tangent space to the Hilbert scheme at a point Y to the local cohomology group. And we use this map to answer affirmatively(after slight modification) a question by Mark Green and Phillip…

For certain manifolds with an involution the mod 2 cohomology ring of the set of fixed points is isomorphic to the cohomology ring of the manifold, up to dividing the degrees by two. Examples include complex projective spaces and…

In this paper we study the "holomorphic K-theory" of a projective variety, which is defined in terms of the homotopy type of spaces of holomorphic maps from the variety to Grassmannians and loop groups. This theory was introduced by Lawson,…

In this paper, we prove an analogue of the Jordan canonical form theorem for a class of $n$-normal operators on complex separable Hilbert spaces in terms of von Neumann's reduction theory. This is a continuation of our study of bounded…

We apply some methods of homology and K-theory to special classes of branes wrapping homologically nontrivial cycles. We treat the classification of four-geometries in terms of compact stabilizers (by analogy with Thurston's classification…

We develop a unifed theory to study geometry of manifolds with different holonomy groups. They are classified by (1) real, complex, quaternion or octonion number they are defined over and (2) being special or not. Specialty is an…