Related papers: Weinstein Handlebodies for the Painlev\'e Betti Sp…

We exhibit the first examples of hyperbolic three-manifolds for which the Seiberg-Witten equations do not admit any irreducible solution. Our approach relies on hyperbolic geometry in an essential way; it combines an explicit upper bound…

We use Donaldson invariants of regular surfaces with p_g >0 to make quantitative statements about modulispaces of stable rank 2 sheaves. We give two examples: a quantitative existence theorem for stable bundles, and a computation of the…

We construct and analyse models of equivariant cohomology for differentiable stacks with Lie group actions extending classical results for smooth manifolds due to Borel, Cartan and Getzler. We also derive various spectral sequences for the…

In this article, we study the dynamical properties of Reeb vector fields on b-contact manifolds. We show that in dimension 3, the number of so-called singular periodic orbits can be prescribed. These constructions illuminate some key…

We study the moduli space of stable sheaves of Euler characteristic 1 supported on curves of arithmetic genus 3 contained in a smooth quadric surface. We show that this moduli space is rational. We compute its Betti numbers by studying the…

We give an explicit Betti presentation of the Stokes torsors attached to meromorphic flat connections of prescribed irregular type along a simple normal crossings divisor, at fixed Kummer level. Our construction is strictly 1-categorical…

Given i.i.d. observations uniformly distributed on a closed submanifold of the Euclidean space, we study higher-order generalizations of graph Laplacians, so-called Hodge Laplacians on graphs, as approximations of the Laplace-Beltrami…

We prove a generalization of Bennequin's inequality for Legendrian knots in a 3-dimensional contact manifold (Y,xi), under the assumption that Y is the boundary of a 4-dimensional manifold M and the version of Seiberg-Witten invariants…

Seidel-Smith and Manolescu constructed knot homology theories using symplectic fibrations whose total spaces were certain varieties of matrices. These knot homology theories were associated to $SL(n) $ and tensor products of the standard…

We prove the genus zero part of the generalized Witten conjecture relating moduli spaces of spin curves to Gelfand-Dickey hierarchies. That is, we show that intersection numbers on the moduli space of stable r-spin curves assemble into a…

We construct an oriented cobordism between moduli spaces of flat connections on the three holed sphere and disjoint unions of toric varieties, together with a closed two-form which restricts to the symplectic forms on the ends. As…

In this article we complete the proof---for a broad class of four-manifolds---of Witten's conjecture that the Donaldson and Seiberg-Witten series coincide, at least through terms of degree less than or equal to c-2, where c is a linear…

A geometric characterization of the structure of the group of automorphisms of an arbitrary Birkhoff-Grothendieck bundle splitting $\bigoplus_{i=1}^{r} \mathcal(m_{i})$ over $\mathbb{C}\mathbb{P}^{1}$ is provided, in terms of its action on…

We study the relationship between several constructions of symplectic realizations of a given Poisson manifold. Our main result is a general formula for a formal symplectic realization in the case of an arbitrary Poisson structure on…

For an elliptic surface $q:Y \to \Sigma$, with prescribed singular fibres, Stefan Bauer proved directly via algebraic geometry that the stable bundles over $Y$, whose chern classes are pull backs from $\Sigma$, correspond to the stable…

Let X be a compact Riemann surface together with a finite set of marked points. We use Morse theoretic techniques to compute the Betti numbers of the parabolic U(2,1)-Higgs bundles moduli spaces over X. We give examples for one marked point…

We present an explicit method to produce upper bounds for the dimension of the moduli spaces of complete integral Gorenstein curves with prescribed symmetric Weierstrass semigroups.

We study Betti numbers of sequences of Riemannian manifolds which Benjamini-Schramm converge to their universal covers. Using the Price inequalities we developed elsewhere, we derive two distinct convergence results. First, under a negative…

We prove that the higher harmonic signature of an even dimensional oriented Riemannian foliation of a compact Riemannian manifold with coefficients in a leafwise U(p,q)-flat complex bundle is a leafwise homotopy invariant. We also prove the…

Co-Higgs bundles are Higgs bundles in the sense of Simpson, but with Higgs fields that take values in the tangent bundle instead of the cotangent bundle. Given a vector bundle on P^1, we find necessary and sufficient conditions on its…