arXiv research

The paper classifies reversible and strongly reversible elements in Hermitian isometry groups.

Classifies reversible and strongly reversible elements in quaternionic groups.

Let $G$ be a group. An element $g$ in $G$ is called reversible if it is conjugate to $g^{-1}$ within $G$, and called strongly reversible if it is conjugate to its inverse by an order two element of $G$. Let $\textbf{H}_{\mathbb H}^n$ be the $n$-dimensional quaternionic hyperbolic space. Let $\mathrm{PSp}(n,1)$ be the i…

This paper classifies reversible and strongly reversible elements in affine groups.

Pairs of elements in quaternionic hyperbolic space have zero measure of being strongly doubly reversible.

The paper classifies reversible elements in Seifert-fibered spaces and braid groups.

The paper classifies and decomposes quaternionic projective transformations.

We call a closed, connected, orientable manifold in one of the categories TOP, PL or DIFF chiral if it does not admit an orientation-reversing automorphism and amphicheiral otherwise. Moreover, we call a manifold strongly chiral if it does not admit a self-map of degree -1. We prove that there are strongly chiral, smoo…

In Garside groups, axes of Morse elements are strongly contracting.

Algebraic method reveals criterion for quaternionic Möbius group reversibility.

Collective behaviours taking place in financial markets reveal strongly correlated states especially during a crisis period. A natural hypothesis is that trend reversals are also driven by mutual influences between the different stock exchanges. Using a maximum entropy approach, we find coordinated behaviour during tre…

A quandle orbit's orientation is problematic when reversed.

Classifies reciprocal elements in Hecke groups, generalizing Sarnak's work.

Established a Hardy inequality on Finsler manifolds.

Study of strongly invertible Legendrian links in contact 3-space.

Study counts and equidistributes geodesic orbits on curved spaces.

In this paper, we study strongly quasiconvex subgroups in a finitely generated $3$--manifold group $π_1(M)$. We prove that if $M$ is a compact, orientable $3$--manifold that does not have a summand supporting the Sol geometry in its sphere-disc decomposition then a finitely generated subgroup $H \le π_1(M)$ has finite …

Study fiber-preserving, orientation-reversing involutions on Seifert fibered 3-manifolds.

This paper is the continuation of [8]. We essentially prove that the familly of strongly causal spacetimes defined in [8] associated to generic achronal subsets in Ein contains all the examples of BTZ multi black-holes. It provides new elements for the global description of these multi black-holes. We also prove that a…

A new framework RTK accelerates diffusion inference by breaking down the process into fewer, more efficient subproblems.

Study on the cobordism distance between knots and their reverses.

New representations of hyperbolic 3-manifold groups into larger groups.

We study the Lipschitz metric on Outer Space and prove that fully irreducible elements of Out(F_n) act by hyperbolic isometries with axes which are strongly contracting. As a corollary, we prove that the axes of fully irreducible automorphisms in the Cayley graph of Out(F_n) are stable, meaning that a quasi-geodesic wi…

New method detects inconsistencies in AHP matrices using triadic preference reversals.

We use the Birman-Ko-Lee presentation of the braid group to show that all closures of strongly quasipositive braids whose normal form contains a positive power of the dual Garside element $δ$ are fibered. We classify links which admit such a braid representative in geometric terms as boundaries of plumbings of positive…

We present a complete classification of elements in the mapping class group of the torus which have a representative that can be written as a product of two orientation reversing involutions. Our interest in such decompositions is motivated by features of the monodromy maps of real fibrations. We employ the property th…

We prove that if $φ,ψ\in Out(F_N)$ are hyperbolic iwips (irreducible with irreducible powers) such that $<φ,ψ>\le Out(F_N)$ is not virtually cyclic then some high powers of $φ$ and $ψ$ generate a free subgroup of rank two, all of whose nontrivial elements are again hyperbolic iwips. Being a hyperbolic iwip element of $…

A polynomial f(t) with rational coefficients is strongly irreducible if f(t^k) is irreducible for all positive integers k. Likewise, two polynomials f and g are strongly coprime if f(t^k) and g(t^l) are relatively prime for all positive integers k and l. We provide some sufficient conditions for strong irreducibility a…

We study minimal energy problems for strongly singular Riesz kernels on a manifold. Based on the spatial energy of harmonic double layer potentials, we are motivated to formulate the natural regularization of such problems by switching to Hadamard's partie finie integral operator which defines a strongly elliptic pseud…

Generic Hitchin representations generate dense subgroups.

A quasi-geodesic is Morse if and only if it is strongly contracting in injective spaces.

Circle graph automorphisms match circle's and are strongly universal.

Pairs trading strategy fails to outperform market benchmarks, but performs well during bear markets.

We prove that both the hyperelliptic mapping class group and the extended hyperelliptic mapping class group are generated by two torsion elements. We also compute the index of the subgroup of the hyperelliptic mapping class group which is generated by involutions and we prove that the extended hyperelliptic mapping cla…

Every closed oriented manifold $M$ is associated with a set of integers $D(M)$, the set of self-mapping degrees of $M$. In this paper we investigate whether a product $M\times N$ admits a self-map of degree $d$, when neither $D(M)$ nor $D(N)$ contains $d$. We find sufficient conditions so that $D(M\times N)$ contains e…

We introduce and systematically study the concept of a growth tight action. This generalizes growth tightness for word metrics as initiated by Grigorchuk and de la Harpe. Given a finitely generated, non-elementary group $G$ acting on a $G$--space $\mathcal{X}$, we prove that if $G$ contains a strongly contracting eleme…

The article explores causal structures in symmetric spaces and their relation to AQFT.

We study the connections among the mapping class group of the twice punctured torus, the cyclic branched coverings of (1,1)-knots and the cyclic presentations of groups. We give the necessary and sufficient conditions for the existence and uniqueness of the n-fold strongly-cyclic branched coverings of (1,1)-knots, thro…

We show that if an orientable Seifert fibered space $M$ with an orientable genus $g$ base space admits a strongly irreducible horizontal Heegaard splitting then there is a one-to-one correspondence between isotopy classes of strongly irreducible horizontal Heegaard splittings and elements of $\mathbf{Z}^{2g}$. The corr…

For an element $Ψ$ in the graded vector space $Ω^*(M, TM)$ of tangent bundle valued forms on a smooth manifold $M$, a $Ψ$-submanifold is defined as a submanifold $N$ of $M$ such that $Ψ_{|N} \in Ω^*(N, TN)$. The class of $Ψ$-submanifolds encompasses calibrated submanifolds, complex submanifolds and all Lie subgroups in…

This paper studies a subgroup of the Goeritz group related to Heegaard splittings induced by openbook decompositions.

Paper analyzes sample complexity for offline $f$-divergence-regularized contextual bandits.

We investigate the problem of characterising the family of strongly quasipositive links which have definite symmetrised Seifert forms and apply our results to the problem of determining when such a link can have an L-space cyclic branched cover. In particular, we show that if $δ_n = σ_1 σ_2 \ldots σ_{n-1}$ is the dual …

Study on achiral Sol 3-manifolds with density results.

Paper combines QRM and CNN for better stock option price forecasting.

Let {a,b} and {c,d} be two pairs of bounding simple closed curves on an oriented surface which intersect nontrivialy. We prove that if these pairs are invariant under the action of an orientation reversing involution, then the corresponding bounding pair maps generate a free group. This supports the conjecture stated b…

This article is a survey on Lorenz knots. We describe the original construction, prove several classical properties, in particular the fact that the closure of a positive braid is a fibered knot, and describe Ghys'correspondance between modular knots and Lorenz knots. We also prove two new properties, namely that follo…

We use commutator techniques and calculations in solvable Lie groups to investigate certain evolution Partial Differential Equations (PDEs for short) that arise in the study of stochastic volatility models for pricing contingent claims on risky assets. In particular, by restricting to domains of bounded volatility, we …