相关论文: The RO(G)-graded coefficients of (Z/2)^n-equivaria…

In this note we present a complete computation of the topological K-theory of the reduced C*-algebra of a semidirect product of the form $\Gamma=\mathbb{Z}^n\rtimes_\rho\mathbb{Z}/2$ with no further assumptions about of the conjugacy action…

We study the relationship between the twisted Orbifold K-theories ${^{\alpha}}K_{orb}(\textsl{X})$ and ${^{\alpha'}}K_{orb}(\textsl{Y})$ for two different twists $\alpha\in Z^3(G;S^1)$ and $\alpha'\in Z^3(G';S^1)$ of the Orbifolds…

We describe Universal Coefficient Theorems for the equivariant Kasparov theory for C*-algebras with an action of the group of integers or over a unique path space, using KK-valued invariants. We compare the resulting classification up to…

We compute the vertical unramified Brauer group of the Galois normic bundles, which are given by $\mathrm{N}_{K/k}(\mathbf{z})=P(x)$. Our main result gives combinatorial formulas for the vertical unramified Brauer groups in terms of the…

This is a review/announcement of results concerning the connection between certain exactly solvable two-dimensional models of statistical mechanics, namely loop models, and the equivariant $K$-theory of the cotangent bundle of the…

Sometimes a homology cycle of a nonsingular compactification manifold cannot be represented by a nonsingular submanifold. We want to know whether such nonrepresentable cycles can be wrapped by D-branes. A brane wrapping a representable…

We adapt Quillen's calculation of graded K-groups of Z-graded rings with support in N to graded K-theory, allowing gradings in a product Z \times G with G an arbitrary group. This in turn allows us to use inductions and calculate graded…

We produce a partial compactification of the variety given by P(t)=N_{K/k}(\mathbf z) whose Brauer group coincides with the unramified Brauer group, where K is an \'etale k-algebra and P(t)\in k[t] is a nonconstant polynomial. Then we…

We introduce a new definition of weighted Grassmann orbifolds. We study their several invariant $q$-cell structures and the orbifold singularities on these $q$-cells. We discuss when the integral cohomology of a weighted Grassmann orbifold…

We analyze the level-rank duality of untwisted and epsilon-twisted D-branes of the so(N)_K WZW model. Untwisted D-branes of so(N)_K are characterized by integrable tensor and spinor representations of so(N)_K. Level-rank duality maps…

In this paper, we study a generalization of twisted (groupoid) equivariant $\mathrm{K}$-theory in the sense of Freed-Moore for $\mathbb{Z}_2$-graded $\mathrm{C}^*$-algebras. It is defined by using Fredholm operators on Hilbert modules with…

We show that all supersymmetric Type IIA D-branes can be constructed as bound states of a certain number of unstable non-supersymmetric Type IIA D9-branes. This string-theoretical construction demonstrates that D-brane charges in Type IIA…

We calculate the excitation spectrumof closed k-strings in 2+1 dimensional SU(N) gauge theories for N = 4, 5 and k = 2. Our results demonstrate that the low-lying spectrum of the k = 2 string falls into sectors that belong to nearly pure…

For $G$ a finite group, a normalized 2-cocycle $\alpha\in Z^{2}\big(G,{\mathbb S}^{1}\big)$ and $X$ a $G$-space on which a normal subgroup $A$ acts trivially, we show that the $\alpha$-twisted $G$-equivariant $K$-theory of $X$ decomposes as…

We systematically revisit the description of $D$-branes on orbifolds and the classification of their charges via K-theory. We include enough details to make the results accessible to both physicists and mathematicians interested in these…

We give a complete classification of T6/[Z(2)xZ(2M)xOmegaR] orientifolds on factorisable tori and rigid D6-branes on them. The analysis includes the supersymmetry, RR tadpole cancellation and K-theory conditions and complete massless open…

We calculate the D-brane superpotentials for two Calabi-Yau manifolds with three deformations by the generalized hypergeometric GKZ systems, which give rise to the flux superpotentials $\mathcal{W}_{GVW}$ of the dual F-theory…

In this paper, we provide an explicit description of the Schubert classes in the equivariant $K$-theory of weighted Grassmann orbifolds. We introduce the `twisted factorial Grothendieck polynomials', a family of symmetric polynomials by…

We show that the number of half-supersymmetric p-branes in the Type II theories compactified on orbifolds is determined by the wrapping rules recently introduced, provided that one accounts correctly for both geometric and non-geometric…

Over an algebraically closed base field $k$ of characteristic 2, the ring $R^G$ of invariants is studied, $G$ being the orthogonal group O(n) or the special orthogonal group SO(n) and acting naturally on the coordinate ring $R$ of the…