Related papers: Cannibalistic Classes of String Bundles

In this article we announce some results on compactifying moduli spaces of rank-2 vector bundles on surfaces by spaces of vector bundles on trees of surfaces. This is thought as an algebraic counterpart of the so called bubbling of vector…

We investigate a holographic realization in Type-IIB string theory of pure Chern-Simons theories, and focus on the level/rank dualities that they enjoy. The level/rank duality is established between the boundary theory, engineered utilizing…

The generalized string topology construction of Gruher and Salvatore assigns to any bundle of $E_n$-algebras $A$ over a closed oriented manifold $M$ a collection of intersection-type operations on the homology of the total space. These…

One describes, using a detailed analysis of Atiyah--Hirzebruch spectral sequence, the tuples of cohomology classes on a compact, complex manifold, corresponding to the Chern classes of a complex vector bundle of stable rank. This…

We show that there is a series of topological string theories whose integrable structure is described by the Toda lattice hierarchy. The monodromy group of the Frobenius manifold for the matter sector is an extension of the affine Weyl…

Given a simply connected manifold $M$, we completely determine which rational monomial Pontryagin numbers are attained by fiber homotopy trivial $M$-bundles over the $k$-sphere, provided that $k$ is small compared to the dimension of $M$.…

A parametrization of (super) moduli space near the corners corresponding to bosonic or Neveu-Schwarz open string degenerations is introduced for worldsheets of arbitrary topology. With this parametrization, Feynman graph polynomials arise…

Greenlees and Sadofsky showed that the classifying spaces of finite groups are self-dual with respect to Morava K-theory K(n). Their duality map was constructed using a transfer map. We generalize their duality map and prove a K(n)-version…

We determine some classes of varieties X - that include the varieties with numerically effective tangent bundle - satisfying the following property: if E is a Higgs bundle such that f*E is semistable for any morphism f from a smooth…

We show that any continuous $\mathbf{C}$-linear Lie algebra splitting of the symbol map from the Atiyah algebra of a vector bundle on a complex manifold is given by a differential operator of order at most the rank of the bundle plus one.…

In this paper we build an Orlik-Solomon model for the canonical gradation of the cohomology algebra with integer coefficients of the complement of a toric arrangement. We give some results on the uniqueness of the representation of…

Representations of vertex operator algebras define sheaves of coinvariants and conformal blocks on moduli of stable pointed curves. Assuming certain finiteness and semisimplicity conditions, we prove that such sheaves satisfy the…

We show that isomorphism classes $[\mathcal{A}]$ of flat $q\times q$ matrix bundles $\mathcal{A}$ (or projectively flat rank-$q$ complex vector bundles $\mathcal{E}$) on a pro-torus $\mathbb{T}$ are in bijective correspondence with the…

We introduce and study translation numbers for automorphisms of principal $\mathbb{Z}$-bundles and flat principal $\mathbb{R}$-bundles. We use them to show a vanishing result of a characteristic class of foliated bundles and to detect…

We attempt to develop a general algebro-geometric study of the moduli stack of commutative, 1-parameter formal Lie groups. We emphasize the pro-algebraic structure of this stack: it is the inverse limit, over varying n, of moduli stacks of…

We define the notion of a trace kernel on a manifold M. Roughly speaking, it is a sheaf on M x M for which the formalism of Hochschild homology applies. We associate a microlocal Euler class to such a kernel, a cohomology class with values…

We prove that the nonvarying strata of abelian and quadratic differentials in [CM1, CM2] have trivial tautological rings and are affine varieties. We also prove that strata of $k$-differentials of infinite area are affine varieties for all…

We obtain relations among the characteristic classes of a manifold M admitting corank one maps. Our relations yield strong restrictions on the cobordism class of M and also nonexistence results for singular maps of the projective spaces. We…

We argue that a generic instability afflicts vacua that arise in theories whose moduli space has large dimension. Specifically, by studying theories with multiple scalar fields we provide numerical evidence that for a generic local minimum…

Representations of certain vertex algebras, here called of CohFT-type, can be used to construct vector bundles of coinvariants and conformal blocks on moduli spaces of stable curves [DGT2]. We show that such bundles define semisimple…