On the cyclic 3-manifold covers of the type surface x R
Abstract
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.
Keywords
Cite
@article{arxiv.2406.15457,
title = {On the cyclic 3-manifold covers of the type surface x R},
author = {Jordan A. Sahattchieve},
journal= {arXiv preprint arXiv:2406.15457},
year = {2024}
}
Comments
The article has 11 pages and contains original mathematical research to be presented at the 41st Workshop in Geometric Topology at Calvin College. It contains no figures