arXiv subjects

Jordan A. Sahattchieve

Publications and source records attributed to Jordan A. Sahattchieve.

3 recordsLinked to original sources

arXiv2025

Solutions to two open problems in geometric group theory

We introduce a method for analyzing the convex hull of a set in non-positively curved piecewise Euclidean polygonal complexes and we apply this method to prove that, with the usual action of Fm x Zn on the metric product of the Cayley graph of Fm with Rn, every quasiconvex subgroup of Fm x Zn is convex. This answers the question whether a quasiconvex subgroup of a CAT(0) group is a CAT(0) group in the affirmative for the groups F m x Zn. We also prove bounded packing in a special class of polycyclic groups, and we introduce the notion of coset growth and provide a bound for the coset growth of uniform lattices in Sol.

math.GR↗

arXiv2024

On the cyclic 3-manifold covers of the type surface x R

This article contains a proof of the fact that, under certain mild technical conditions, the action of the automorphism group of a cyclic 3-manifold cover of the type SxR, where S is a compact surface, yields a compact quotient. This result is then immediately applied to extend a theorem on the fiberings over the circle of certain compact 3-manifolds which are torus sums. As a corollary, I prove the validity of the conditional main theorem in my article titled "A fibering theorem for 3-manifolds", which appeared in the Journal of Groups, Complexity, Cryptology in 2021 and its subsequent erratum. This paper also furnishes a proof of the irreducibility of the summands of compact 3-manifolds which are torus sums and irreducible, and a proof of the interesting observation that a compact connected orientable 3-manifold whose fundamental group contains a subnormal subgroup of infinite index is the connected sum of an irreducible compact 3-manifold with (finitely many) 3-balls.

math.GM↗

arXiv2023

A fibering theorem for 3-manifolds

An erratum to this article is posted at https://gcc.episciences.org/page/errata This paper generalizes results of M. Moon on the fibering of certain compact 3-manifolds over the circle. It also generalizes a theorem of H. B. Griffiths on the fibering of certain 2-manifolds over the circle.

math.GT↗