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.
The paper classifies diffeomorphism classes of Calabi-Yau threefolds constructed by gluing methods.
We prove that smooth 1-dimensional topological field theories over a manifold are equivalent to vector bundles with connection. The main novelty is our definition of the smooth 1-dimensional bordism category, which encodes cutting laws rather than gluing laws. We make this idea precise through a smooth version of Rezk'…
Study examines heart and football-shaped metrics, verifying geometric structure.
We give a differential-geometric construction and examples of Calabi-Yau threefolds, at least one of which is {\it{new}}. Ingredients in our construction are {\it admissible pairs}, which were dealt with by Kovalev in \cite{K03} and further studied by Kovalev and Lee in \cite{KL11}. An admissible pair $(\overline{X},D)…
We give a differential-geometric construction of compact manifolds with holonomy which is based on Joyce's second construction of compact -manifolds in \cite{Joyce00} and Kovalev's gluing construction of -manifolds in \cite{Kovalev03}. We also give some examples of compact $\ma…
The closure conditions of the inexact exterior differential form and dual form (an equality to zero of differentials of these forms) can be treated as a definition of some differential-geometrical structure. Such a connection discloses the properties and specific features of the differential-geometrical structures. The…
We study differential geometric properties of cuspidal edges with boundary. There are several differential geometric invariants which are related with the behavior of the boundary in addition to usual differential geometric invariants of cuspidal edges. We study the relation of these invariants with several other invar…
We give a differential-geometric construction of Calabi-Yau fourfolds by the `doubling' method, which was introduced in \cite{DY14} to construct Calabi-Yau threefolds. We also give examples of Calabi-Yau fourfolds from toric Fano fourfolds. Ingredients in our construction are \emph{admissible pairs}, which were first d…
This paper treats the theory of Mukai duality on K3 surfaces from the differential geometric perspective, taylored to the need of the author's companion paper about Mukai duality of adiabatic coassociative K3 fibrations.
The paper discusses conditions for gluing multiple Alexandrov spaces into an Alexandrov space.
We compute the differential geometric invariants of cuspidal edges on flat surfaces in hyperbolic -space and in de Sitter space. Several dualities of invariants are pointed out.
Study on knots formed by gluing ellipses, defining gluing degree.
We investigate learning of the differential geometric structure of a data manifold embedded in a high-dimensional Euclidean space. We first analyze kernel-based algorithms and show that under the usual regularizations, non-probabilistic methods cannot recover the differential geometric structure, but instead find mostl…
New PL invariant classifies K3 surface degenerations.
Some model reduction techniques for multiple time-scale dynamical systems make use of the identification of low dimensional slow invariant attracting manifolds (SIAM) in order to reduce the dimensionality of the phase space by restriction to the slow flow. The focus of this work is on a proposition and discussion of a …
Study geometry of surfaces glued along a curve.
Contact gluing maps are shown to be equivalent in sutured Floer homology.
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 …
Based on the theory of Poisson vertex algebras we calculate skew-symmetry conditions and Jacobi identities for a class of third-order nonlocal operators of differential-geometric type. Hamiltonian operators within this class are defined by a Monge metric and a skew-symmetric two-form satisfying a number of differential…
The differential geometric aspects of Geometric Phases are reviewed.
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.
Evolutionary forms, as well as exterior forms, are skew-symmetric differential forms. But in contrast to the exterior forms, the basis of evolutionary forms is deforming manifolds (with unclosed metric forms). Such forms possess a peculiarity, namely, the closed inexact exterior forms are obtained from that. The closur…
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.
Study geometric properties of S1 singularities and their deformations.
The exposition has been significantly altered, hopefully improved.
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…
Simplified proof of gluing formula for analytic torsion forms.
Constructs a solution operator for hyperbolic gluing in higher dimensions.
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…
We implement a differential-geometric approach to normal forms for contracting measurable cocycles to $\mbox{Diff}^q({\bf R}^n, {\bf 0})$, . We obtain resonance polynomial normal forms for the contracting cocycle and its centralizer, via changes of coordinates. These are interpreted as nonstationary inv…
Differential geomtrical methods for deriving the Dirac equation in Curved Spacetime are presented. Einstein's field equation is applied in a novel manner; in the most current standard reference, Birrell and Davies, 1994 [1], the suggestions for deriving the Dirac equation in Curved Spacetime make no mention of employin…
Gluing theorem for collapsing warped-QAC Calabi-Yau manifolds verified.
Paper discusses gluing formula for zeta-determinants with Robin boundary condition.
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…
Study gluing event horizons of Minkowski and Schwarzschild spacetimes.
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 …
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…
The paper simplifies FLRW photon propagators using geometric embeddings.