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 constructs trisections for fiber bundles over a circle.
Study on hyperelliptic Lefschetz fibrations, finding singular fiber counts.
New exotic 4-manifolds found with fiber bundles.
In this note, we compute the virtual first Betti numbers of 4-manifolds fibering over with prime fiber. As an application, we show that if such a manifold is symplectic with nonpositive Kodaira dimension, then the fiber itself is a sphere or torus bundle over . In a different direction, we prove that if the …
Study Lefschetz fibrations with 4D fibers using Seiberg-Witten theory.
Study uses twisted Alexander polynomials to link fibered classes in 3-manifolds.
Around 1920, Kaluza and Klein had the idea to add a fifth dimension to the classical 4-dimensional spacetime of general relativity to create a geometric theory of gravitation and electromagnetism. Today, theoretical evidences, like string theory, suggest the need for a spacetime with more than five dimensions. We want …
Calegari's 4-spheres from fibered knots are proven standard.
We prove the additivity of the Casson-Seiberg-Witten invariant of integral homology under fiber sum along embedded curves and embedded tori, which is the -dimensional analogue of the additivity of the Casson invariant under connected-sum and splicing along knots.
The paper proves conditions for self-covering manifolds to be fiber bundles over a circle.
For each d>=2, the mapping class group for plane curves of degree d will be defined and it is proved that there exists uniquely the Meyer function on this group. In the case of d=4, using our Meyer function, we can define the local signature for 4-dimensional fiber spaces whose general fibers are non-hyperelliptic comp…
New Fueter sections solve monopole equations for 3/2-spinors.
New 4D homeomorphism shows surprising similarities to 2D.
The paper conjectures a 4D characterization of tight contact structures and proves it for certain cases.
The study constructs and analyzes new symplectic 4-manifolds from hyperelliptic Lefschetz fibrations.
Bryant and Salamon gave a construction of metrics of G2 holonomy on the total space of the bundle of anti-self-dual (ASD) 2-forms over a 4-dimensional self-dual Einstein manifold. We generalise it by considering the total space of an SO(3) bundle (with fibers R^3) over a 4-dimensional base, with a connection on this bu…
In analogy with the vector bundle theory we define universal and strongly universal Lefschetz fibrations over bounded surfaces. After giving a characterization of these fibrations we construct very special strongly universal Lefschetz fibrations when the fiber is the torus or an orientable surface with connected bounda…
New singularity theorems are derived for generic warped-product spacetimes of any dimension. The main purpose is to analyze the stability of (compact or large) extra dimensions against dynamical perturbations. To that end, the base of the warped product is assumed to be our visible 4-dimensional world, while the extra …
We study the invariants of surfaces in 4-manifolds extracted from the Seiberg-Witten and the Ozsvath-Szabo invariants of their fiber sums with auxiliary Lefschetz fibrations. Such invariants involve relative Spin_c structures and can be treated as refinements of the usual Seiberg-Witten and Ozsvath-Szabo invariants. We…
The study characterizes and classifies specific types of manifolds using conformal and quasi-Einstein properties.
We propose in this paper a new approach to the Kaluza-Klein idea of a five dimensional space-time unifying gravitation and electromagnetism, and extension to higher-dimensional space-time. By considering a natural geometric definition of a matter fluid and abandoning the usual requirement of a Ricci-flat five dimension…
New relation found in 4D symplectic mapping class group.
Nonorientable 4-manifolds can be fibred over 2-disks with nonorientable fibers.
Donaldson showed that every closed symplectic 4-manifold can be given the structure of a topological Lefschetz pencil. Gay and Kirby showed that every closed 4-manifold has a trisection. In this paper we relate these two structure theorems, showing how to construct a trisection directly from a topological Lefschetz pen…
The goal of this paper is to construct distinct trisections of the same genus on a fixed 4-manifold. For every , we construct non-diffeomorphic -trisections on infinitely many 4-manifolds. Here, the manifolds are spun Seifert fiber spaces and the trisections come from Meier's spun trisection…
Proof outlined for 4D smooth Poincaré conjecture.
The paper defines and characterizes 2-Ruled hypersurfaces in Minkowski 4-space using octonions.
The paper calculates transformation operators and proves a theorem on 4D manifolds.
The study classifies 331 specific 4D polytopes with 7 facets.
We give a curvature identity derived from the generalized Gauss-Bonnet formula for 4-dimensional compact oriented Riemannian manifolds. We prove that the curvature identity holds on any 4-dimensional Riemannian manifold which is not necessarily compact. We also provide some applications of the identity.
We compare the invariants of flat vector bundles defined by Atiyah et al. and Jones et al. and prove that, up to weak homotopy, they induce the same map, denoted by , from the -connective algebraic -theory space of the complex numbers to the homotopy fiber of the Chern character. We examine homotopy properties…
The paper introduces new inequalities for knots in 4D cobordisms.
We give an elementary proof of the fact that any 4-dimensional para-Hermitian manifold admits a unique para-Kaehler--Weyl structure. We then use analytic continuation to pass from the para-complex to the complex setting and thereby show any 4-dimensional pseudo-Hermitian manifold also admits a unique Kaehler--Weyl stru…
A weakly Einstein manifold is a generalization of a 4-dimensional Einstein manifold, which is defined as an application of a curvature identity derived from the generalized Gauss-Bonnet formula for a 4-dimensional compact oriented Riemannian manifold. In this paper, we shall give a characterization of a weakly Einstein…
The Ooguri-Vafa space is a 4-dimensional incomplete hyperkähler manifold, defined on the total space of a singular torus fibration with one singular nodal fiber. It has been proposed that the Ooguri-Vafa hyperkähler metric should be part of the local model of the hyperkähler metric of the Hitchin moduli spaces, near th…
Classifies metrics on specific Lie groups.
The goal of this article is to study the pinching problem proposed by S.-T. Yau in 1990 replacing sectional curvature by one weaker condition on biorthogonal curvature. Moreover, we classify 4-dimensional compact oriented Riemannian manifolds with nonnegative biorthogonal curvature. In particular, we obtain a partial a…
We show that the Spivak normal fibration of an orientable 4-dimensional Poincaré complex has a vector bundle reduction.
Maps from 4D handlebodies to their boundaries have sections.
We classify up to automorphisms all left-invariant non-Einstein solutions to the Einstein--Maxwell equations on 4-dimensional Lie algebras.
4D theorem for disks, generalizing previous work.
The paper characterizes and contrasts knots with high 4D clasp numbers.
Global regularity proved for 4D Ricci flow with scalar curvature integral bound.
The object of investigations are almost hypercomplex structures with Hermitian-Norden metrics on 4-dimensional Lie groups considered as smooth manifolds. There are studied both the basic classes of a classification of 4-dimensional indecomposable real Lie algebras depending on two parameters. Some geometric characteris…
A 4-dimensional Riemannian manifold equipped with an endomorphism of the tangent bundle, whose fourth power is the identity, is considered. The matrix of this structure in some basis is circulant and the structure acts as an isometry with respect to the metric. Such manifolds are constructed on 4-dimensional real Lie g…
We investigate proper biharmonic hypersurfaces with at most three distinct principal curvatures in space forms. We obtain the full classification of proper biharmonic hypersurfaces in 4-dimensional space forms.
In this paper we will construct a Weierstrass type representation for minimal surfaces in 4-dimensional Lorentzian Damek-Ricci spaces and we give some examples of such surfaces.
Withdrawn May 2005. There is an error in the even-dimensional case of the proof in the April 2005 version. The hoped-for 4-dimensional applications are unlikely to survive the repairs.