相关论文: The correspondence induced on the pillowcase by th…

We prove that the restriction map from the subspace of regular points of the holonomy perturbed SU(2) traceless flat moduli space of a tangle in a 3-manifold to the traceless flat moduli space of its boundary marked surface is a Lagrangian…

We examine the holonomy-perturbed traceless SU(2) character variety of the trivial four-stranded tangle {p_1,p_2,p_3,p_4} X [0,1] in S^2 X [0,1] equipped with a strong marking, either an earring or a bypass. Viewing these marked tangles as…

We introduce explicit holonomy perturbations of the Chern-Simons functional on a 3-ball containing a pair of unknotted arcs. These perturbations give us a concrete local method for making the moduli spaces of flat singular SO(3) connections…

Given a 2-stranded tangle in a $\ZZ/2$ homology ball, $T\subset Y$, we investigate the character variety $R(Y,T)$ of conjugacy classes of traceless SU(2) representations of $\pi_1(Y\setminus T)$. In particular we completely determine the…

In this paper we give the first example of a surface bundle over a surface with at least three fiberings. In fact, for each $n \ge 3$ we construct $4$-manifolds $E$ admitting at least $n$ distinct fiberings $p_i: E \to \Sigma_{g_i}$ as a…

We consider the moduli space of bordered Riemann surfaces with boundary and marked points. Such spaces appear in open-closed string theory, particularly with respect to holomorphic curves with Lagrangian submanifolds. We consider a…

The traceless $SU(2)$ character variety $R(S^2,\{a_i,b_i\}_{i=1}^n)$ of a $2n$-punctured 2-sphere is the symplectic reduction of a Hamiltonian $n$-torus action on the $SU(2)$ character variety of a closed surface of genus $n$. It is…

We investigate the assembly of the dipole-like patchy particles confined to a spherical surface by Brownian dynamics simulations. The surface property of the spherical particle is described by the spherical harmonic $Y_{10}$, and the…

If a link $L$ can be decomposed into the union of two tangles $T\cup_{S^2} S$ along a 2-sphere intersecting $L$ in 4 points, then the intersections of perturbed traceless SU(2) character varieties of tangles in a space called the pillowcase…

Special kinds of rank 2 vector bundles with (possibly irregular) connections on P^1 are considered. We construct an equivalence between the derived category of quasi-coherent sheaves on the moduli stack of such bundles and the derived…

We define an elementary relatively $\mathbb Z/4$ graded Lagrangian-Floer chain complex for restricted immersions of compact 1-manifolds into the pillowcase, and apply it to the intersection diagram obtained by taking traceless $SU(2)$…

In earlier work we have shown that the moduli space $N$ of flat connections for the (trivial) $\roman{SU(2)}$-bundle on a closed surface of genus $\ell \geq 2$ inherits a structure of stratified symplectic space with two connected strata…

A submanifold is said to be tangentially biharmonic if the bitension field of the isometric immersion that defines the submanifold has vanishing tangential component. The purpose of this paper is to prove that a surface in Euclidean…

We construct an algebraic version of Lagrangian Floer homology for immersed curves inside the pillowcase. We first associate to the pillowcase an algebra A. Then to an immersed curve L inside the pillowcase we associate an A infinity module…

A Tangle is a smooth simple closed curve formed from arcs (or ``links'') of circles with fixed radius. Most previous study of Tangles has dealt with the case where these arcs are quarter-circles, but Tangles comprised of thirds and sixths…

Let $M$ be the moduli space of rank 3 parabolic vector bundles over a Riemann surface with several punctures. By the Mehta-Seshadri correspondence, this is the space of rank 3 unitary representations of the fundamental group of the…

On a Riemann surface of genus $> 1$, we discuss how to construct opers with apparent singularities from $SL_2(\mathbb{C})$ $\lambda$-connections $(E, \nabla_\lambda)$ and sub-line bundles $L$ of $E$. This construction defines a rational map…

We present a pair of smooth fiber bundles over the circle with a common $4$-dimensional fiber with the following properties: (1) their total spaces are diffeomorphic to each other; (2) they are isomorphic to each other as topological fiber…

In a recent experiment Campbell et al. [Phys. Rev. Lett. 96, 020406 (2006)] observed degenerate four-wave mixing of matter-waves in a one-dimensional optical lattice, a process with potential for generating entanglement among atoms. We…

The buckling of elastic bodies is a common phenomenon in the mechanics of solids. Wrinkling of membranes can often be interpreted as buckling under constraints that prohibit large amplitude deformation. We present a combination of analytic…