A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Researchers prove a nonlinear gluing theorem for gravitational fields near static backgrounds.
Gluing theorem for collapsing warped-QAC Calabi-Yau manifolds verified.
The paper discusses conditions for gluing multiple Alexandrov spaces into an Alexandrov space.
The paper extends gluing theorems for gravitational fields in higher dimensions.
New method glues Lorentzian spaces, preserving curvature bounds.
Butscher, D. Lee, Y. Lee, and Joyce constructed a special Lagrangian submanifold by gluing a Lawlor neck into a transverse intersection point of two special Lagrangian submanifolds. We prove a uniqueness theorem for the gluing of flat special Lagrangian tori of real dimension 3 in a flat complex torus of complex dimens…
The paper extends gluing theorems for linearized gravitational fields in static spacetimes with cosmological constant.
We prove gluing theorems for tight contact structures. In particular, we rederive (as special cases) gluing theorems due to Colin and Makar-Limanov, and present an algorithm for determining whether a given contact structure on a handlebody is tight. As applications, we construct a tight contact structure on a genus 4 h…
In this paper we announce a gluing theorem for conformal structures with anti-self-dual (ASD) Weyl tensor that applies in geometrical situations that are more general than those considered by previous authors. By adapting a method proposed by Floer, sufficient conditions are given for the existence of ASD conformal str…
The purpose of this paper is to prove a gluing theorem for a given special Lagrangian submanifold of a Calabi-Yau 3-fold. The proof will be an adaption of the gluing techniques in J-holomorphic curve theory. It is a well known procedure in geometric analysis to construct new solutions to a given nonlinear partial diffe…
Extends ASD connection existence to 4-manifolds with cylindrical ends.
Extends Perelman's theorem to positive intermediate curvature conditions.
Abstract: Lipschitz homeomorphisms are deformed using Perelman's methods.
`Gluing' is a technique of constructing solutions to non-linear (elliptic) partial differential equations such as Yang--Mills equations, minimal surface equations and Einstein equations. Calibrated submanifolds are a certain class of minimal surfaces, and there are various examples of them constructed by the gluing tec…
Third paper in series defines monopole Floer homology and gluing theorem for 3-manifolds.
The purpose of this paper is to give an application of the gluing theorem for special Lagrangian submanifolds of a Calabi-Yau 3-fold. We proved a gluing theorem before to smooth a codimension-two singularity of a particular special Lagrangian submanifold. In this paper we will show that this theorem can be applied to m…
Surveying mass in 2D hyperbolic geometry, overcoming challenges via minimisation.
New signs and gradings enable detailed comparison in Heegaard Floer theory.
Local gluing connects flow lines in finite time intervals.
Survey on gluing constructions under lower curvature bounds.
We use the construction of unfolded Seiberg-Witten Floer spectra of general 3-manifolds defined in our previous paper to extend the notion of relative Bauer-Furuta invariants to general 4-manifolds with boundary. One of the main purposes of this paper is to give a detailed proof of the gluing theorem for the relative i…
Paper proves gluing formula for analytic torsions using Witten deformation for non-Morse functions.
We give new and rather general gluing theorems for anti-self-dual (ASD) conformal structures, following the method suggested by Floer. The main result is a gluing theorem for pairs of conformally ASD manifolds `joined' across a common piece (union of connected components) of their boundaries. This theorem genuinely ope…
Method constructs rigid associative submanifolds in twisted G2-manifolds.
In this paper we construct Ricci-positive metrics on the connected sum of products of arbitrarily many spheres provided the dimensions of all but one sphere in each summand are at least 3. There are two new technical theorems required to extend previous results on sums of products of two spheres. The first theorem is a…
In 2002, Isenberg-Mazzeo-Pollack (IMP) constructed a series of vacuum initial data sets via a gluing construction. In this paper, we investigate some local geometry of these initial data sets as well as implications regarding their spacetime developments. In particular, we state conditions for the existence of outer tr…
We study partial collapsing degeneration of Hamiltonian-perturbed Floer trajectories for an adiabatic -family and its reversal adiabatic gluing, as the prototype of the partial collapsing degeneration of -dimensional (perturbed) -holomorphic maps to -dimensional gradient segments. We consider the …
We develop a gluing construction which adds scaled and truncated asymptotically Euclidean solutions of the Einstein constraint equations to compact solutions with potentially non-trivial cosmological constants. The result is a one-parameter family of initial data which has ordinary and scaled "point-particle" limits an…
Smoothly attaches manifolds with controlled curvature.
In the present paper, we establish a gluing construction for the Nahm pole solutions to the Kapustin-Witten equations over manifolds with boundaries and cylindrical ends. Given two Nahm pole solutions with some convergence assumptions on the cylindrical ends, we prove that there exists an obstruction class for gluing t…
We prove a Lipschitz-Volume rigidity theorem in Alexandrov geometry, that is, if a 1-Lipschitz map between Alexandrov spaces preserves volume, then it is a path isometry and an isometry when restricted to the interior of . We furthermore characterize the metric structure on with re…
Study on moduli spaces of Seiberg-Witten equations on manifolds with boundary.
We introduce a class of combinatorial hypersurfaces in the complex projective space. They are submanifolds of codimension~2 in $\C P^n$ and are topologically "glued" out of algebraic hypersurfaces in $(\C^*)^n$. Our construction can be viewed as a version of the Viro gluing theorem, relating topology of algebraic hyper…
The invariant was first introduced by E. Artal, V. Florens and the author. Inspired by the idea of G. Rybnikov, we obtain a multiplicativity theorem of this invariant under the gluing of two arrangements along a triangle. An application of this theorem is to prove that the extended Rybnik…
Perelman's doubling theorem asserts that the metric space obtained by gluing along their boundaries two copies of an Alexandrov space with curvature is an Alexandrov space with the same dimension and satisfying the same curvature lower bound. We show that this result cannot be extended to metric measure spaces…
Develops gluing theory for contact instantons and pseudoholomorphic curves.
The study resolves a conjecture about harmonic forms on compact manifolds.
This is the second part of an article in two parts, which builds the foundation of a Floer-theoretic invariant, I_F. (See math.DG/0111313 for part I). Having constructed I_F and outlined a proof of its invariance based on bifurcation analysis in part I, in this part we prove a series of gluing theorems to confirm the b…
We give a combinatorial proof of a theorem first proved by Souto which says the following. Let M_1 and M_2 be simple 3-manifolds with connected boundary of genus g>0. If M_1 and M_2 are glued via a complicated map, then every minimal Heegaard splitting of the resulting closed 3-manifold is an amalgamation. This proof a…
We give a completely formalized definition of a notion of " general manifold ". It turns out that " gluing data " form an equivalence-partially ordered set (e-pos), which is a special instance of an ordered groupoid. We state and prove reconstruction theorems, allowing to reconstruct general manifolds and their mor-phi…
This paper and its sequel prove a generalization of the usual gluing theorem for two index 1 pseudoholomorphic curves u_+ and u_- in the symplectization of a contact 3-manifold. We assume that for each embedded Reeb orbit gamma, the total multiplicity of the negative ends of u_+ at covers of gamma agrees with the total…
This is the third installment in our series of articles (dg-ga/9712005, dg-ga/9710032) on the application of the PU(2) monopole equations to prove Witten's conjecture (hep-th/9411102) concerning the relation between the Donaldson and Seiberg-Witten invariants of smooth four-manifolds. The moduli space of solutions to t…
Several proofs have been published of the Mod Z gluing formula for the eta-invariant of a Dirac operator. However, so far the integer contribution to the gluing formula for the eta-invariant is left obscure in the literature. In this article we present a gluing formula for the eta-invariant which expresses the integer …
We establish a gluing theorem for monopoles over 4--manifolds containing long necks. The theorem is stated in terms of an ungluing map defined explicitly in terms of data that appear naturally in applications. Orientations of moduli spaces are handled using Benevieri--Furi's concept of orientations of Fredholm operator…
Our goal is to show the beauty and power of Alexandrov geometry by reaching interesting applications and theorems with a minimum of preparation. The topics include 1. Reshetnyak's gluing theorem, 2. Estimates on the number of collisions in billiards, 3. Reshetnyak's majorization theorem, 4. Hadamard--Cartan globalizati…
Inspired by the work of Boris Vertman on refined analytic torsion for manifolds with boundary, in this paper we extend the construction of the Cappell-Miller analytic torsion to manifolds with boundary. We also compare it with the refined analytic torsion on manifolds with boundary. As a byproduct of the gluing formula…
We prove a gluing theorem for solutions of Hitchin's self-duality equations with logarithmic singularities on a rank-2 vector bundle over a noded Riemann surface representing a boundary point of Teichmüller moduli space.
We prove equality between the renormalized Ray-Singer analytic torsion and the intersection R-torsion on a Witt-manifold with cusps, up to an error term determined explicitly by the Betti numbers of the cross section of the cusp and the intersection R-torsion of a model cone. In the first step of the proof we compute e…