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.
A Heegaard splitting of a closed, orientable three-manifold satisfies the disjoint curve property if the splitting surface contains an essential simple closed curve and each handlebody contains an essential disk disjoint from this curve [Thompson, 1999]. A splitting is full if it does not have the disjoint curve proper…
This paper studies properties of weak reducing pairs in critical Heegaard splittings.
Study vortex flows on Riemann surfaces, proving dominated splitting and Anosov properties.
Paper develops a splitting principle for RCD spaces, extending manifold properties.
Using basic properties of one-sided Heegaard splittings, a direct proof that geometrically compressible one-sided splittings of RP^3 are stabilised is given. The argument is modelled on that used by Waldhausen to show that two-sided splittings of S^3 are standard.
Let M be a totally orientable graph manifold with characteristic submanifold T and let M = V cup_S W be a Heegaard splitting. We prove that S is standard. In particular, S is the amalgamation of strongly irreducible Heegaard splittings. The splitting surfaces S_i of these strongly irreducible Heegaard splittings have t…
Minimal splitting factors help study scalar curvature constraints.
The paper defines a condition for the finiteness of mapping class groups of Heegaard splittings.
Metric spaces with certain curvature properties are universally infinitesimally Hilbertian.
Study various series of groups and their Lie algebras in split extensions.
Introduces nonlinear splittings on fibre bundles for generalizing connections.
A Heegaard diagram for a 3-manifold is regarded as a pair of simplexes in the complex of curves on a surface and a Heegaard splitting as a pair of subcomplexes generated by the equivalent diagrams. We relate geometric and combinatorial properties of these subcomplexes with topological properties of the manifold and/or …
The paper reveals a property of chromatic homology for complete graphs.
Study series invariants for plumbed 3-manifolds and their properties.
We investigate the concordance properties of `parallel links' P(K), given by the (2,0) cable of a knot K. We focus on the question: if P(K) is concordant to a split link, is K necessarily slice? We show that if P(K) is smoothly concordant to a split link, then many smooth concordance invariants of K must vanish, includ…
We prove a Lorentzian splitting theorem with weakened curvature conditions.
The hierarchical Dirichlet process (HDP) has become an important Bayesian nonparametric model for grouped data, such as document collections. The HDP is used to construct a flexible mixed-membership model where the number of components is determined by the data. As for most Bayesian nonparametric models, exact posterio…
Histogram binning method proven with guarantees without splitting data.
The paper examines when 2-string tangles can be embedded into specific link types.
A gap in a paper of Rubinstein-Scharlemann is explored: new examples are found of closed orientable 3-manifolds with possibly multiple genus 2 Heegaard splittings. Properties common to all the examples in the original paper are not universally shared by the new examples: some of the new examples have Hempel distance 3,…
New methods improve prediction regions for high-dimensional data.
We study intrinsically linked graphs where we require that every embedding of the graph contains not just a non-split link, but a link that satisfies some additional property. Examples of properties we address in this paper are: a two component link with lk(A,L) = k2^r, k not 0, a non-split n-component link where all l…
We provide necessary conditions for the Alexander polynomials of algebraically split component-preservingly amphicheiral links. We raise a conjecture that the Alexander polynomial of an algebraically split component-preservingly amphicheiral link with even components is zero. Our necessary conditions and some examples …
IMPaCT improves node classification in chronological split temporal graphs.
We construct a sequence of pairs of 3-manifolds each with torus boundary and with the following two properties: 1) For the result of a carefully chosen glueing of the nth pair of 3-manifolds along their boundary tori, the ratio of the genus of the resulting 3-manifold to the sum of the genera of the pair of 3-manifolds…
Let be a compact orientable irreducible 3-manifold and be an unstabilized genus three Heegaard splitting of . In this article, we will define a simplicial complex of weak reducing pairs for and find several properties of this complex. Using this method, we will prove that an unstabilized Heegaard splitti…
In this paper we study CAT(0) groups and their splittings as graphs of groups. For one-ended CAT(0) groups with isolated flats we prove a theorem characterizing exactly when the visual boundary is locally connected. This characterization depends on whether the group has a certain type of splitting over a virtually abel…
It is shown that if the exterior of a link L in the three sphere admits a genus 2 Heegaard splitting, then L has Generalized Property R.
We record various properties of twisted Becker-Gottlieb transfer maps and study their multiplicative properties analogous to Becker-Gottlieb transfer. We show these twisted transfer maps factorise through Becker-Schultz-Mann-Miller-Miller transfer; some of these might be well known. We apply this to show that $BSO(2n+1…
The paper proves a theorem about splitting manifolds with specific curvature properties.
Study curvature properties of w.a. S-manifolds with new conditions.
New GLPs split Lévy bridges into non-overlapping subprocesses.
Synthetic splitting theorem for Lorentzian spaces with non-negative curvature.
This paper studies the Riley polynomial of 2-bridge knots using Chebyshev polynomials.
In this paper, we generalize topological results known for noncompact manifolds with nonnegative Ricci curvature to spaces with nonnegative -Bakry Émery Ricci curvature. We study the Splitting Theorem and a property called the geodesic loops to infinity property in relation to spaces with nonnegative -Bakry Émery…
SBAMDT uses adaptive soft splits to model complex decision boundaries.
In this paper we study some splitting properties on complete noncompact manifolds with smooth measures when -dimensional Bakry-Émery Ricci curvature is bounded from below by some negative constant and spectrum of the weighted Laplacian has a positive lower bound. These results extend the cases of Ricci curvatur…
Novel methods for splitting Gaussian mixtures improve uncertainty propagation in nonlinear systems.
The paper explores how splitting data samples influences optimal neural network hyperparameters.
Minimal Morse functions on Poincaré dodecahedral space are selected via spectral properties.
PD_3-groups split as HNN extensions, revealing homology class properties.
Invariant counts maximum stable umbilic splits.
New splitting theorems in a semi-Riemannian manifold which admits an irrotational vector field (not necessarily a gradient) with some suitable properties are obtained. According to the extras hypothesis assumed on the vector field, we can get twisted, warped or direct decompositions. Some applications to Lorentzian man…
We give a simple criterion for a Heegaard splitting to yield a Haken manifold. As a consequence, we construct many Haken manifolds, in particular homology spheres, with prescribed properties, namely Heegaard genus, Heegaard distance and Casson invariant. Along the way we give simpler and shorter proofs of the existence…
New perspective on Heegaard splittings using square complexes and combinatorial measurements.
Researchers describe and compare decompositions of Poincaré duality pairs.
Develops a new inference method for split-sample estimators using multiple splits.
We prove that random groups in the Gromov density model, at any density, satisfy property (FA), i.e. they do not act non-trivially on trees. This implies that their Gromov boundaries, defined at density less than 1/2, are Menger curves.