Related papers: Multiplicative Quantum Cobordism Theory

We describe a construction of Gromov-Witten invariants for flag varieties and use it to give a presentation for the quantum cohomology ring, by extending the ideas used by Bertram in the case of Grassmannians. This provides a proof for the…

We prove a formula for the push-forward class of Bott-Samelson resolutions in the algebraic cobordism ring of the flag bundle. We specialise our formula to connective K-theory providing a geometric interpretation to the double…

We prove a general form of the statement that the cohomology of a quotient stack can be computed by the Borel construction. It also applies to the lisse extensions of generalized cohomology theories like motivic cohomology and algebraic…

Let G denote a complex, semisimple, simply-connected group. We identify the equivariant quantum differential equation for the cotangent bundle to the flag variety of G with the affine Knizhnik-Zamolodchikov connection of Cherednik and…

We offer here a more direct approach to twisted K-theory, based on the notion of twisted vector bundles (of finite or infinite dimension) and of twisted principal bundles. This is closeely related to the classical notion ot torsors and…

Commutative K-theory, a cohomology theory built from spaces of commuting matrices, has been explored in recent work of Adem, G\'{o}mez, Gritschacher, Lind, and Tillman. In this article, we use unstable methods to construct explicit…

Let $K$ be a finite group and let $G$ be a finite group acting on $K$ by automorphisms. In this paper we study two different but intimately related subjects: on the one side we classify all possible multiplicative and associative structures…

This is a study of twisted K-theory on a product space $T \times M$. The twisting comes from a decomposable cup product class which applies the 1-cohomology of $T$ and the 2-cohomology of $M$. In the case of a topological product, we give a…

We prove that the Schubert structure constants of the quantum $K$-theory ring of any minuscule flag variety or quadric hypersurface have signs that alternate with codimension. We also prove that the powers of the deformation parameter $q$…

We develop equivariant KK-theory for locally compact groupoid actions by Morita equivalences on real and complex graded C*-algebras. Functoriality with respect to generalised morphisms and Bott periodicity are discussed. We introduce…

Given a vector bundle $F$ on a smooth Deligne-Mumford stack $\X$ and an invertible multiplicative characteristic class $\bc$, we define the orbifold Gromov-Witten invariants of $\X$ twisted by $F$ and $\bc$. We prove a "quantum Riemann-Roch…

We introduce a general framework to unify several variants of twisted topological $K$-theory. We focus on the role of finite dimensional real simple algebras with a product-preserving involution, showing that Grothendieck-Witt groups…

A strong version of the quantization conjecture of Guillemin and Sternberg is proved. For a reductive group action on a smooth, compact, polarized variety (X,L), the cohomologies of L over the GIT quotient X // G equal the invariant part of…

Let X=G/P be a homogeneous space and e_k be the class of a simple coroot in H_2(X). A theorem of Strickland shows that for almost all X, the variety of pointed lines of degree e_k, denoted Z_k(X), is again a homogeneous space. For these X…

We introduce and study a $K$-theory of twisted bundles for associative algebras $A(\mathfrak g)$ of formal series with an infinite-Lie algebra coefficients over arbitrary compact topological spaces. Fibers of such bundles are given by…

Quantum K-theory is a K-theoretic version of quantum cohomology, which was recently defined by Y.-P. Lee. Based on a presentation for the quantum K-theory of the classical flag variety Fl_n, we define and study quantum Grothendieck…

We conjecture that appropriate K-theoretic Gromov-Witten invariants of complex flag manifolds G/B are governed by finite-difference versions of Toda systems constructed in terms of the Langlands-dual quantized universal enveloping algebras…

In algebraic geometry, Gromov--Witten invariants are enumerative invariants that count the number of complex curves in a smooth projective variety satisfying some incidence conditions. In 2001, A. Givental and Y.P. Lee defined new…

It has been proposed that cobordism and K-theory groups, which can be mathematically related in certain cases, are physically associated to generalised higher-form symmetries. As a consequence, they should be broken or gauged in any…

We introduce a periodic form of the iterated algebraic K-theory of ku, the (connective) complex K-theory spectrum, as well as a natural twisting of this cohomology theory by higher gerbes. Furthermore, we prove a form of topological…