Related papers: The caloron correspondence and higher string class…

Let M be a connected, simply connected, closed and oriented manifold, and G a finite group acting on M by orientation preserving diffeomorphisms. In this paper we show an explicit ring isomorphism between the orbifold string topology of the…

We describe a categorical framework for the classification of D-branes on noncommutative spaces using techniques from bivariant K-theory of C*-algebras. We present a new description of bivariant K-theory in terms of noncommutative…

For a compact Riemannian locally symmetric space $\Gamma\backslash G/K$ of arbitrary rank we determine the location of certain Ruelle-Taylor resonances for the Weyl chamber action. We provide a Weyl-lower bound on an appropriate counting…

Calorons (periodic instantons) interpolate between monopoles and instantons, and their holonomy gives approximate Skyrmion configurations. We show that, for each caloron charge N \leq 4, there exists a one-parameter family of calorons which…

In this note, we first explain the equivalence between the interaction Hamiltonian of Green-Schwarz light-cone gauge superstring field theory and the twist field formalism known from matrix string theory. We analyze the role of the large N…

Given a closed monotone symplectic manifold $M$, we define certain characteristic cohomology classes of the free loop space $L \text {Ham}(M, \omega)$ with values in $QH_* (M)$, and their $S^1$ equivariant version. These classes generalize…

We determine the holonomy of generalized Killing spinor covariant derivatives of the form $D= \nabla + \Omega$ on pseudo-Riemannian reductive homogeneous spaces in a purely algebraic and algorithmic way, where $\Omega : TM \rightarrow…

In this paper we propose a theory of contact invariants and open string invariants, which are generalizations of the relative invariants. We introduce two moduli spaces $\bar{\mathcal{M}}_{A}(M^{+},C,g,m+\nu,{\bf y},{\bf…

For a discrete group G, we represent the Bredon cohomology with local coefficients as the homotopy classes of maps in the category of equivaraint crossed complexes. Subsequently, we construct a naive parametrized G-spectrum, such that the…

In a 2009 paper, Dave Benson gave a description in purely algebraic terms of the mod $p$ homology of $\Omega(BG^\wedge_p)$, when $G$ is a finite group, $BG^\wedge_p$ is the $p$-completion of its classifying space, and $\Omega(BG^\wedge_p)$…

We review recent progress in string cosmology, where string dualities are applied so as to obtain complete cosmological evolutions, free of any essential singularities. Two classes of models are analyzed. The first class consists of string…

In this paper we introduce the Cheeger-Simons cohomology of a global quotient orbifold. We prove that the Cheeger-Simons cohomology of the orbifold is isomorphic to its Beilinson-Deligne cohomology. Furthermore we construct a string…

Let $G$ be a simply-connected, simple compact Lie group of type $\{n_{1},\ldots,n_{\ell}\}$, where $n_{1}\le\cdots \le n_{\ell}$. Let $\mathcal{G}_k$ be the gauge group of the principal $G$-bundle (namedright{P}{}{S^{4}}) whose isomorphism…

We derive a map relating the gauge symmetry groups of heterotic strings on $T^4$ to other components of the moduli space with rank reduction. This generalizes the results for $T^2$ and $T^3$ which mirror the singularity freezing mechanism…

In this paper we define a Poisson structure on some moduli spaces related to principal G-bundles on elliptic curves, the simplest example being the moduli space of stable pairs: a vector bundle and its global section. We also study…

For a finite group $G$, we compute the algebraic $K$-theory of the category of equivariant sheaves on a locally compact Hausdorff $G$-space, generalizing a result of Efimov, and determine the equivariant $E$-theory of the $C^*$-algebra of…

We introduce differentiable stacks and explain the relationship with Lie groupoids. Then we study $S^1$-bundles and $S^1$-gerbes over differentiable stacks. In particular, we establish the relationship between $S^1$-gerbes and groupoid…

The theories of strings and $D$-branes have motivated the development of non Abelian cohomology techniques in differential geometry, on the purpose to find a geometric interpretation of characteristic classes. The spaces studied here, like…

For a commutative noetherian ring R, we investigate relations between tilting and cotilting modules in Mod-R and Mod-R_m where m runs over the maximal spectrum of R. For each finite n, we construct a 1-1 correspondence between (equivalence…

Given a closed simply connected manifold $M$ of dimension $2n\ge6$, we compare the ring of characteristic classes of smooth oriented bundles with fibre $M$ to the analogous ring resulting from replacing $M$ by the connected sum…