Related papers: A JSJ splitting for triangulated open 3-manifolds

According to the Weinstein splitting theorem, any Poisson manifold is locally, near any given point, a product of a symplectic manifold with another Poisson manifold whose Poisson structure vanishes at the point. Similar splitting results…

This paper describes a generalization of decomposition in orbifolds. In general terms, decomposition states that two-dimensional orbifolds and gauge theories whose gauge groups have trivially-acting subgroups decompose into disjoint unions…

We derive a necessary and sufficient condition for the separability of tripartite three mode Gaussian states, that is easy to check for any such state. We give a classification of the separability properties of those systems and show how to…

This survey examines separation of variables for algebraically integrable Hamiltonian systems whose tori are Jacobians of Riemann surfaces. For these cases there is a natural class of systems which admit separations in a nice geometric…

We show that after one stabilization, a strongly irreducible Heegaard splitting of suitably large genus of a graph manifold is isotopic to an amalgamation along a modified version of the system of canonical tori in the JSJ decomposition. As…

We introduce multisections of smooth, closed 4-manifolds, which generalize trisections to decompositions with more than three pieces. This decomposition describes an arbitrary smooth, closed 4-manifold as a sequence of cut systems on a…

We show that open 3-manifolds that have a locally finite decomposition along 2-spheres are characterized by the existence of a Riemannian metric with respect to which the second homotopy group of the manifold is generated by small elements.

We classify smooth Fano threefolds that admit degenerations to toric Fano threefolds with ordinary double points.

The operation of crushing a normal surface has proven to be a powerful tool in computational $3$-manifold topology, with applications both to triangulation complexity and to algorithms. The main difficulty with crushing is that it can…

For each integer k > 1, Johnson gave a 3-manifold with Heegaard splittings of genera 2k and 2k-1 such that any common stabilization of these two surfaces has genus at least 3k-1. We modify his argument to produce a 3-manifold with two…

We generalize Poisson-Nijenhuis structures. We prove that on a manifold endowed with a Nijenhuis tensor and a Jacobi structure which are compatible, there is a hierarchy of pairwise compatible Jacobi structures. Furthermore, we study the…

This paper gives sharp linear bounds on the genus of a normal surface in a triangulated compact, orientable 3--manifold in terms of the quadrilaterals in its cell decomposition---different bounds arise from varying hypotheses on the surface…

In the kinematic region where three particles $i$, $j$, $k$ are collinear, the multi-parton scattering amplitudes factorise into a product of a triple collinear splitting function and a multi-parton scattering amplitude with two fewer…

A triangulation of a polygon has an associated Stanley-Reisner ideal. We obtain a full algebraic and combinatorial understanding of these ideals, and describe their separated models. More generally we do this for stacked simplicial…

In this note, we find a necessary condition on odd-dimensional Riemannian manifolds under which both of Sasakian structure and the generalised Ricci soliton equation are satisfied, and we give some examples.

The aim of this paper is to prove a normal form Theorem for Dirac-Jacobi bundles using the recent techniques from Bursztyn, Lima and Meinrenken. As the most important consequence, we can prove the splitting theorems of Jacobi pairs which…

We adapt for algebraically closed fields $k$ of characteristic greater than $2$ two results of Voisin, on the decomposition of the diagonal of a smooth cubic hypersurface $X$ of dimension $3$ over $\mathbb C$, namely: the equivalence…

We find sufficient conditions for a principal toric bundle over compact K\"ahler manifolds to admit Calabi-Yau connections with torsion. With the aids of a topological classification, we construct such geometry on $n(S^2\times…

From the view of Heegaard splitting, it is known that if a closed orientable 3-manifold admits a distance at least three Heegaard splitting, then it is hyperbolic. However, for a closed orientable 3-manifold admitting only distance at most…

Let $M$ be a closed orientable 3-manifold with a genus two Heegaard splitting $(V_1, V_2; F)$ and a non-trivial JSJ-decomposition, where all components of the intersection of the JSJ-tori and $V_i$ are not $\partial$-parallel in $V_i$ for…