Related papers: ECH spectrum of some prequantization bundles

We present a local combinatorial formula for the Euler class of a $n$-dimen\-si\-onal PL spherical fiber bundle as a rational number $e_{\it CH}$ associated to a chain of $n+1$ abstract subdivisions of abstract $n$-spherical PL cell…

The idea of a line bundle in classical geometry is transferred to noncommutative geometry by the idea of a Morita context. From this we can construct Z and N graded algebras, the Z graded algebra being a Hopf-Galois extension. A…

In this article we calculate the dimension of the Hilbert space of Kahler quantization of the moduli space of vortices on a Riemann surface. This dimension is given by the holomorphic Euler characteristic of the quantum line bundle.

A convex chain is a finite integer linear combination of indicator functions of convex polytopes. Khovanskii-Pukhlikov extend the Ehrhart theory of convex lattice polytopes to the setting of convex chains. Extending the relationship between…

We define the notion of a parahoric group scheme $\mathcal G$ over a smooth projective curve, and formulate four conjectures on the structure of the stack of $\mathcal G$-bundles, which generalize to this case well-known results on…

In the first part we use Gromov's K--area to define the K--area homology which stabilizes into singular homology on the category of pairs of compact smooth manifolds. The second part treats the questions of certain curvature gaps. For…

For an $\E$-ring spectrum $R$ and a map $f:X\to Pic(R)$ of spaces, the Thom spectrum $\T f$ is a comodule over $R\otimes\Si X$. In this parper we study the topological coHochschild homology of $R\otimes\Si X$ with coefficient $\T f$. More…

We study the orientability of vector bundles with respect to a family of cohomology theories called $\mathrm{EO}$-theories. The $\mathrm{EO}$-theories are higher height analogues of real $\mathrm{K}$-theory $\mathrm{KO}$. For each…

Using higher topos theory, we explore the obstruction to the \v{C}ech-de Rham map being an isomorphism in each degree for diffeological spaces. In degree 1, we obtain an exact sequence which interprets Iglesias-Zemmour's construction from…

For the moduli spaces of Abelian differentials, the Euler characteristic is one of the most basic intrinsic topological invariants. We give a formula for the Euler characteristic that relies on intersection theory on the smooth…

In this paper we define 2-vector bundles as suitable bundles of 2-vector spaces over a base space, and compare the resulting 2-K-theory with the algebraic K-theory spectrum K(V) of the 2-category of 2-vector spaces, as well as the algebraic…

We consider the moduli space of vector bundles of rank $n$ and degree $ng$ over a fixed Riemann surface of genus $g\geq 2$. We use the explicit parametrization in terms of the Tyurin data. In the moduli space there is a "non-abelian" Theta…

We consider a generalized chiral Gaussian Unitary Ensemble (chGUE) based on a weak confining potential. We study the spectral correlations close to the origin in the thermodynamic limit. We show that for eigenvalues separated up to the mean…

In this note we compute the cohomology of the elliptic tangent bundle, a Lie algebroid used to describe singular symplectic forms arising from generalized complex geometry.

Let $G$ be a complex connected reductive algebraic group that acts on a smooth complex algebraic variety $X$, and let $E$ be a $G$-equivariant algebraic vector bundle over $X$. A section of $E$ is regular if it is transversal to the zero…

Using a covariant description of the geometry of deformations for extendons, it is shown that the topological corrections for the string action associated with the Euler characteristic and the first Chern number of the normal bundle of the…

Gorenstein toric contact manifolds are good toric contact manifolds with zero first Chern class that are completely determined by certain integral convex polytopes called toric diagrams. The Ehrhart polynomial of these toric diagrams…

We study sheaves E on a smooth projective curve X which are minimal with respect to the property that $h^0(E \otimes L) >0$ for all line bundles L of degree zero. We show that these sheaves define ample divisors D(E) on the Picard torus…

The Quillen-Bismut-Freed construction associates a determinant line bundle with connection to an infinite dimensional super vector bundle with a family of Dirac-type operators. We define the regularized first Chern form of the infinite…

We calculate the Euler characteristics of all of the Teichmuller curves in the moduli space of genus two Riemann surfaces which are generated by holomorphic one-forms with a single double zero. These curves can all be embedded in Hilbert…