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 sets lower bounds for a Kirby-Thompson invariant of 4-manifolds.
problem Determining the Kirby-Thompson invariant of specific 4-manifolds.
method Using trisections, the paper establishes lower bounds and calculates the invariant for specific examples.
result The paper calculates the Kirby-Thompson invariant of the spin of L(2,1) and shows the existence of 4-manifolds with arbitrarily large invariants.
In this paper, invariant submanifolds of a generalized Kenmotsu manifold are studied. Necessary and sufficient conditions are given on a submanifold of a generalized Kenmotsu manifold to be an invariant submanifold.In this case, we investigate further properties of invariant submanifolds of \ a generalized Kenmotsu man…
Framework extends sutured manifold invariants to pairs with torus boundaries.
problem Extending sutured manifold invariants to pairs with torus boundaries.
method Establishing a framework for extending invariants of sutured manifolds to pairs of sutured manifolds differing by attaching a basic slice along a torus boundary.
result Framework recovers bordered-sutured Floer homology for a corresponding bordered-sutured three-manifold.
Paper connects two invariants of 3D manifolds using Hopf algebras.
problem Establishing a relation between two invariants of 3D manifolds.
method Using spherical Hopf algebras and their Drinfeld doubles, the paper connects the chromatic spherical invariant and the Hennings-Kauffman-Radford invariant.
result The chromatic spherical invariant is equal to the Hennings-Kauffman-Radford invariant for a specific type of Hopf algebra.
Study Θ-invariants for spherical 3-manifolds via Zπ-homology equivalences.
problem Computing Θ-invariants for spherical 3-manifolds via Zπ-homology equivalences.
method Using Bott and Cattaneo's Θ-invariants, defined by integrals over configuration spaces with local systems, and representation theory of finite groups.
result Computed upper bounds for dimensions of spaces spanned by Θ-invariants and finite type invariants.
As a generalization of Riemannian submersions, horizontally conformal submersions, semi-invariant submersions, h-semi-invariant submersions, almost h-semi-invariant submersions, conformal semi-invariant submersions, we introduce h-conformal semi-invariant submersions and almost h-conformal semi-invariant submersions fr…
The Kuperberg invariant is a topological invariant of closed 3-manifolds based on finite-dimensional Hopf algebras. In this paper, we initiate the program of constructing 4-manifold invariants in the spirit of Kuperberg's 3-manifold invariant. We utilize a structure called a Hopf triplet, which consists of three Hopf a…
The t-invariant can be considered as the Turaev-Viro invariant of order 5 computed for integer colors only. We compute all values of the t-invariant for Seifert manifolds with base sphere and three singular fibers. As a result we show that the manifolds parameters modulo five define the value of the t-invariant. Partia…
We introduce anti-invariant Riemannian submersions from Sasakian manifolds onto Riemannian manifolds. We survey main results of anti-invariant Riemannian submersions defined on Sasakian manifolds. We investigate necessary and sufficient condition for an anti-invariant Riemannian submersion to be totally geodesic and ha…
We introduce anti-invariant Riemannian submersions from cosymplectic manifolds onto Riemannian manifolds. We survey main results of anti-invariant Riemannian submersions defined on cosymplectic manifolds. We investigate necessary and sufficient condition for an anti-invariant Riemannian submersion to be totally geodesi…
Properties of invariant, anti-invariant and slant isometrically immersed submanifolds of metallic Riemannian manifolds are given with a special view towards the induced Σ-structure. Examples of such metallic manifolds are also given.
Study on Δ invariants of plumbed 3-manifolds, comparing with Heegaard-Floer homology.
problem Analyzing Δ invariants of plumbed 3-manifolds.
method Expressing Δ of Seifert manifolds in terms of singularity theory invariants, providing examples for non-Seifert manifolds, comparing with Heegaard-Floer homology.
result Interesting behavior of Δ invariants for non-Seifert manifolds, comparison with Heegaard-Floer homology.
We define a relative Yamabe invariant of a smooth manifold with given conformal class on its boundary. In the case of empty boundary the invariant coincides with the classic Yamabe invariant. We develop approximation technique which leads to gluing theorems of two manifolds along their boundaries for the relative Yamab…
On a smooth closed oriented 4-manifold M with a smooth action of a finite group G on a Spinc structure, G-monopole invariant is defined by "counting" G-invariant solutions of Seiberg-Witten equations for any G-invariant Riemannian metric on M. We compute G-monopole invariants on some G-manifolds. F…
If a real value invariant of compact combinatorial manifolds (with or without boundary) depends only on the number of simplices in each dimension on the manifold, then the invariant is completely determined by Euler characteristics of the manifold and its boundary. So essentially, Euler characteristic is the unique inv…
B. Sahin [9] introduced the notion of anti-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. In the present paper we extend the notion of anti-invariant and Lagrangian Riemannian submersions (a special anti-invariant Riemannian submersion) to the case of locally conformal Kaehl…