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.
Homogeneous Fano manifolds with specific bundle properties proven.
The paper studies Einstein metrics on specific manifolds and their rigidity properties.
The paper defines a new invariant for links and uses it to show non-sliceness.
The purpose of this paper is to study finite dimensional equivariant moduli problems from the viewpoint of stratification theory. We show that there exists a stratified obstruction system for a finite dimensional equivariant moduli problem. In addition, we define a coindex for a G-vector bundle which is determined by t…
Defines coupled embeddability for maps on products of spaces, generating examples and nonexamples.
The paper studies stability of Einstein metrics on non-simple Lie group homogeneous spaces.
We study the linear stability of Einstein metrics of Riemannian submersion type. First, we derive a general instability condition for such Einstein metrics and provide some applications. Then we study instability arising from Riemannian product structures on the base. As an application, we estimate the coindex of the E…
New Einstein metrics identified on a specific full flag manifold.
Study on stability of non-diagonal Einstein metrics on specific homogeneous spaces.
Counterexample disproves Borde-Sorkin conjecture on causal continuity of Morse spacetimes.
We prove a semi-Riemannian version of the celebrated Morse Index Theorem for geodesics in semi-Riemannian manifolds; we consider the general case of both endpoints variable on two submanifolds. The key role of the theory is played by the notion of the {\em Maslov index} of a semi-Riemannian geodesic, which is a homolog…
Adjacency defined for three-manifolds, linking them to the 3-sphere.
Alternative proof of Dynnikov's three-page index for torus links.
The paper classifies Ricci solitons on specific Lorentzian Lie groups.
We study three-dimensional Alexandrov spaces with a lower curvature bound, focusing on extending three classical results on three-dimensional manifolds: First, we show that a closed three-dimensional Alexandrov space of positive curvature, with at least one topological singularity, must be homeomorphic to the suspensio…
We show that a free period three action on the three-sphere is standard, i.e. the quotient is homeomorphic to a lens space. We use a minimax argument involving sweepouts.
New proof finds three divergence-free vector fields for any 3D manifold.
It is shown that any closed three-manifold M obtained by integral surgery on a knot in the three-sphere can always be constructed from integral surgeries on a 3-component link L with each component being an unknot in the three-sphere. It is also interesting to notice that infinitely many different integral surgeries on…
We construct four-dimensional symplectic cobordisms between contact three-manifolds generalizing an example of Eliashberg. One key feature is that any handlebody decomposition of one of these cobordisms must involve three-handles. The other key feature is that these cobordisms contain chains of symplectically embedded …
The Laplace spectrum uniquely identifies five out of eight metrically maximal three-dimensional geometries.
We prove two rigidity results for complete Riemannian three-manifolds of higher rank. Complete three-manifolds have higher spherical rank if an only if they are spherical space forms. Complete finite volume three-manifolds have higher hyperbolic rank if and only if they are hyperbolic space forms.
We show that a free period three action on a lens space is standard, i.e. the quotient is homeomorphic to a lens space. This is an extension of the result for period three actions on the three-sphere, arXiv:math.GT/0204077, by the author and J. Hyam Rubinstein.
Sharp inequality found on three-balls for fourth order Sobolev traces.
Proves rigidity for eigenvalue estimate on three-manifolds.
We construct a series of finitely presented semigroups. The centers of these semigroups encode uniquely up to rigid ambient isotopy in 3-space all non-oriented spatial graphs. This encoding is obtained by using three-page embeddings of graphs into the product of the line with the cone on three points. By exploiting thr…
Extends three circle theorem to almost Hermitian manifolds.
We explicitly compute the lower algebraic K-theory of the split three-dimensional crystallographic groups; i.e., the groups G that act properly and cocompactly on three-dimensional Euclidean space by isometries, such that the natural map from G to O(3) is a split injection onto its image. There are 73 split three-dimen…
Computes the decomposition of rank-three bundles over the projective line with three marked points.
The paper classifies 3D Lorentzian Lie groups.
Innovates a three-component link homotopy invariant.
Motivated by classical theorems on minimal surface theory in compact hyperbolic three-manifolds, we investigate the questions of existence and deformations for least area minimal surfaces in complete noncompact hyperbolic three-manifold of finite volume. We prove any closed immersed incompressible surface can be deform…
We study three-dimensional generalized Ricci solitons, both in Riemannian and Lorentzian settings. We shall determine their homogeneous models, classifying left-invariant generalized Ricci solitons on three-dimensional Lie groups.
A branched covering surface-knot is a surface-knot in the form of a branched covering over a surface-knot. For a branched covering surface-knot, we have a numerical invariant called the simplifying number. We show that branched covering surface-knots with degree three have the simplifying numbers less than three.
Study finds index of symmetry for solvable 3D Lie groups with left-invariant metrics.
The paper proves three circles theorems and Liouville type theorems for subharmonic and holomorphic functions.
New proof for higher rank subvarieties in genus three.
Constructs a family of genus three minimal surfaces with parallel ends.
The paper explores actions on metric spaces similar to 3D manifolds, proving rigidity results.
We discuss the existence of the angle between two curves in Teichmüller spaces and show that, in any infinite dimensional Teichmüller space, there exist infinitely many geodesic triangles each of which has the same three vertices and satisfies the property that its three sides have the same and arbitrarily given length…
We show that the equivalence problem for three-dimensional Lorentzian manifolds requires at most the fifth covariant derivative of the curvature tensor. We prove that this bound is sharp by exhibiting a class of 3D Lorentzian manifolds which realize this bound. The analysis is based on a three-dimensional analogue of t…
In this paper, we study spinor Frenet equations in three dimensional Lie Groups with a bi-invariant metric. Also, we obtain spinor Frenet equations for special cases of three dimensional Lie groups.
We introduce canonical principal parameters on any strongly regular minimal surface in the three dimensional sphere and prove that any such a surface is determined up to a motion by its normal curvature function satisfying the Sinh-Poisson equation. We obtain a classification theorem for bi-umbilical hypersurfaces of t…
Shells resist three out of six possible loads if simply connected.
We determine which three-manifolds are dominated by products. The result is that a closed, oriented, connected three-manifold is dominated by a product if and only if it is finitely covered either by a product or by a connected sum of copies of the product of the two-sphere and the circle. This characterization can als…
The paper characterizes stable cohomotopy groups in codimensions two and three, linking algebraic and geometric perspectives.
Study left invariant Lorentzian metrics on 3D non-unimodular Lie groups.
In this article, we find the complete list of all contact structures (up to isotopy) on closed three-manifolds which are supported by an open book decomposition having planar pages with three (but not less) boundary components. We distinguish them by computing their first Chern classes and three dimensional invariants …
The paper proves the existence of at least 4 embedded minimal tori in a three-sphere with positive Ricci curvature.