Year: 2025
Type: preprint
Abstract: This paper examines the representations of hyperbolic integral homology spheres into the binary icosahedral group $2I$. We specifically give a geometric meaning to $2I$ representations by relating them to Larsen's notion of quotient dimension, which gives us a sense of the frequency of regular finite covers. Our main theorem shows that hyperbolic 3-manifolds can only have quotient dimension 2 or 3, and each case is obtained infinitely many times. More specifically, we show that those with no non-trivial $A_5$ representations have quotient dimension 3, and we find a family of hyperbolic 3-manifolds obtained by Dehn surgery on an infinite 2-bridge hyperbolic knot family with quotient dimension 2.
Source: arXiv (Cornell University)
Author: Stuebner, Maria
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4407359150