arXiv research

Study on knots formed by gluing ellipses, defining gluing degree.

Study geometry of surfaces glued along a curve.

Study gluing of Lorentzian length spaces and their causal ladder properties.

In a previous article we studied PGL(n,C)-representations of a 3-manifold via a generalization of Thurston's gluing equations. Neumann has proved some symplectic properties of Thurston's gluing equations that play an important role in recent developments of exact and perturbative Chern-Simons theory. In this paper, we …

Constructs a solution operator for hyperbolic gluing in higher dimensions.

Study series invariants for plumbed 3-manifolds and their properties.

We study partial collapsing degeneration of Hamiltonian-perturbed Floer trajectories for an adiabatic $\varepsilon$-family and its reversal adiabatic gluing, as the prototype of the partial collapsing degeneration of $2$-dimensional (perturbed) $J$-holomorphic maps to $1$-dimensional gradient segments. We consider the …

We provide a new topological interpretation of the symplectic properties of gluing equations for triangulations of hyperbolic 3-manifolds, first discovered by Neumann and Zagier. We also extend the symplectic properties to more general gluings of PGL(2,C) flat connections on the boundaries of 3-manifolds with topologic…

We describe the natural gluing map on sutured Floer homology which is induced by the inclusion of one sutured manifold (M',Γ') into a larger sutured manifold (M,Γ), together with a contact structure on M-M'. As an application of this gluing map, we produce a (1+1)-dimensional TQFT by dimensional reduction and study its…

We show that there is a fully faithful embedding of the category of manifolds with corners into the Cahiers topos, one of the premier models for Synthetic Differential Geometry. This embedding is shown to have a number of nice properties, such as preservation of open covers and transverse fibre products. We develop a t…

The paper discusses conditions for gluing multiple Alexandrov spaces into an Alexandrov space.

Paper studies solutions to a specific equation in conformal geometry with singular sets.

Defines new Heegaard Floer invariants with actions of both E and F.

We study Veech groups of covering surfaces of primitive translation surfaces. Therefore we define congruence subgroups in Veech groups of primitive translation surfaces using their action on the homology with entries in $\mathbb{Z}/a\mathbb{Z}$. We introduce a congruence level definition and a property of a primitive t…

Study elliptic operators on glued manifolds, reducing to finite-dimensional systems.

Analytic surgery and gluing formula for torsion forms in fiber bundles.

Paper introduces a new invariant for virtual knotoids and proves it's a Vassiliev invariant of order one.

Contact gluing maps are shown to be equivalent in sutured Floer homology.

We consider sequences of open Riemannian manifolds with boundary that have no regularity conditions on the boundary. To define a reasonable notion of a limit of such a sequence, we examine "$δ$ inner regions" which avoid the boundary by a distance $δ$. We prove Gromov-Hausdorff compactness theorems for sequences of the…

Paper glues characteristic data to Kerr spacetime, proving spacelike gluing.

We determine the adjoint trace field of gluings of general hyperbolic manifolds. This provides a new method to prove the nonarithmeticity of gluings, which can be applied to the classical construction of Gromov and Piatetski-Shapiro (and generalizations) as well as certain gluings of pieces of commensurable arithmetic …

In this paper, we explore the theme of orbifold stratified spaces and establish a general criterion for them to be smooth orbifolds. This criterion utilizes the notion of linear stratification on the gluing bundles for the orbifold stratified spaces. We introduce a concept of good gluing structure to ensure a smooth st…

The paper constructs gluing maps for harmonic maps between Riemannian manifolds.

Researchers prove a nonlinear gluing theorem for gravitational fields near static backgrounds.

Formulae connect heat kernels on glued manifolds.

Solves C^3 null gluing problem for Einstein vacuum equations.

Paper solves Einstein vacuum equations gluing problem with applications.

We survey known (and unknown) results about the behavior of Heegaard genus of 3-manifolds constructed via various gluings. The constructions we consider are (1) gluing together two 3-manifolds with incompressible boundary, (2) gluing together the boundary components of surface times I, and (3) gluing a handlebody to th…

Uniform elliptic theory for Dirac operators on orbifold resolutions.

Simplified proof of gluing formula for analytic torsion forms.

Study general hyperbolic gluings, proving quasi-arithmeticity of building blocks.

The paper classifies surfaces formed by quadrilateral gluings.

We present a gluing formula for Gromov-Witten invariants in the case of a triple product. This gluing formula is a simple case of a much more general gluing formula proved and stated using exploded manifolds. We present this simple case because it is relatively easy to explain without any knowledge of exploded manifold…

Adds charged black holes to de Sitter space.

This paper studies the associativity of gluing of trajectories in Morse theory. We show that the associativity of gluing follows from of the existence of compatible manifold with face structures on the compactified moduli spaces. Using our previous work, we obtain the associativity of gluing in certain cases. In partic…

Gluing theorem for collapsing warped-QAC Calabi-Yau manifolds verified.

Associated to a closed, oriented surface S is the complex vector space with basis the set of all compact, oriented 3-manifolds which it bounds. Gluing along S defines a Hermitian pairing on this space with values in the complex vector space with basis all closed, oriented 3-manifolds. The main result in this paper is t…

Paper discusses gluing formula for zeta-determinants with Robin boundary condition.

Constructs new connections with finite energy in 4D, preserving gauge equivalence and curvature properties.

Survey on gluing constructions under lower curvature bounds.

We study how a gluing construction, which produces compact manifolds with holonomy G_2 from matching pairs of asymptotically cylindrical G_2-manifolds, behaves under deformations. We show that the gluing construction defines a smooth map from a moduli space of gluing data to the moduli space of torsion-free G_2-structu…

Thurston introduced a technique for finding and deforming three-dimensional hyperbolic structures by gluing together ideal tetrahedra. We generalize this technique to study families of geometric structures that transition from hyperbolic to anti de Sitter (AdS) geometry. Our approach involves solving Thurston's gluing …

Study gluing event horizons of Minkowski and Schwarzschild spacetimes.

We study gluings of asymptotically cylindrical special Lagrangian submanifolds in asymptotically cylindrical Calabi--Yau manifolds. We prove both that there is a well-defined gluing map, and, after reviewing the deformation theory for special Lagrangians, prove that this gluing map defines a local diffeomorphism from m…

Gromov has shown how to construct holomorphic maps of the plane to a complex manifold with prescribed values on a lattice. In the present paper, a similar interpolation theorem for pseudo-holomorphic maps from the cylinder S to an almost-complex manifold (M,J) is proved. Properties of the space of pseudo-holomorphic ma…

We study the critical points of the renormalized volume for acylindrical geometrically finite hyperbolic 3-manifolds that include rank-1 cusps, and show that the renormalized volume is locally convex around these critical points. We give a modified definition of the renormalized volume that is additive under gluing, an…

Local gluing connects flow lines in finite time intervals.

In 1978, Gibbons-Pope and Page proposed a physical picture for the Ricci flat Kähler metrics on the K3 surface based on a gluing construction. In this construction, one starts from a flat torus with $16$ orbifold points, and resolves the orbifold singularities by gluing in $16$ small Eguchi-Hanson manifolds which all h…