相关论文: Maslov index formulas for Whitney n-gons

We study certain top intersection products on the Hilbert scheme of points on a nonsingular surface relative to an effective smooth divisor. We find a formula relating these numbers to the corresponding intersection numbers on the…

We investigate soliton collisions in the Manakov model, which is a system of coupled nonlinear Schroedinger equations that is integrable via the inverse scattering method. Computing the asymptotic forms of the general N-soliton solution in…

A multisection of a 4-manifold is a decomposition into 1-handlebodies intersecting pairwise along 3-dimensional handlebodies or along a central closed surface; this generalizes the Gay-Kirby trisections. We show how to compute the twisted…

We calculate the Chern-Simons invariants of the twist knot orbifolds using the Schl\"{a}fli formula for the generalized Chern-Simons function on the family of the twist knot cone-manifold structures. Following the general instruction of…

To determine the relative position of any two surfaces in a system, one approach is to useoperations (Minkowski sum and intersection) on sets of constraints. These constraints aremade compliant with half-spaces of R^n where each set of…

The Maslov index of a periodic orbit is an important piece in the semiclassical quantization of non-integrable systems, while almost all existing techniques that lead to a rigorous calculation of this index are elaborate and mathematically…

Maslov indices are integers that appear in semiclassical wave functions and quantization conditions. They are often notoriously difficult to compute. We present methods of computing the Maslov index that rely only on typically elementary…

We compute the Kazhdan-Lusztig polynomial of the uniform matroid of rank n-1 on n elements by proving that the i-th coefficient of is equal to the number of ways to choose i non-intersecting chords in an (n-i+1)-gon. We also show that the…

In previous work we computed the symplectic volume of the symplectic reduced space of the product of N adjoint orbits of a compact Lie group. In this paper we compute the intersection pairings of the same object.

A fast algorithm for counting intersections of two normal curves on a triangulated surface is proposed. It yields a convenient way for treating mapping class groups of punctured surfaces by presenting mapping classes by matrices, and the…

We derive asymptotic formulas for the solutions of the mixed boundary value problem for the Poisson equation on the union of a thin cylindrical plate and several thin cylindrical rods. One of the ends of each rod is set into a hole in the…

We use the notion of generalized signatures at a singularity of a smooth curve of symmetric bilinear forms to determine a formula for the computation of the Maslov index in the case of a real-analytic path having possibly non transversal…

We compute all the Chern, Milnor and Pontryagin numbers for canonical toric manifolds associated with abstract simplicial complexes and the Stiefel-Whitney numbers for their real counterparts. Applications include combinatorial…

The intersection of two orthogonal cylinders represents a classical problem in computational geometry with direct applications to engineering design, manufacturing, and numerical simulation. While analytical solutions exist for the fully…

This paper solves the combinatorics relating the intersection theory of $\psi$-classes of Hassett spaces to that of $\overline{\mathcal{M}}_{g,n}$. A generating function for intersection numbers of $\psi$ classes on all Hassett spaces is…

In this article we consider a variant of Rabinowitz Floer homology in order to define a homological count of discriminant points for paths of contactomorphisms. The growth rate of this count can be seen as an analogue of Givental's…

We use the properties of the Leray index to give precise formulas in arbitrary dimensions for the Maslov index of the monodromy matrix arising in periodic Hamiltonian systems. We compare our index with other indices appearing in the…

We calculate intersection forms of all 4-dimensional almost-flat manifolds

We investigate the N=2 superconformal index for supersymmetric quiver Chern-Simons theories with large N gauge groups. After general arguments about the large N limit, we compute the first few terms in the series expansion of the index for…

We derive a new explicit formula in terms of sums over graphs for the $n$-point correlation functions of general formal weighted double Hurwitz numbers coming from the Kadomtsev-Petviashvili tau functions of hypergeometric type (also known…