Hecke's Theorem on the Different for $3$-Manifolds
Number Theory
2022-06-02 v1 Geometric Topology
Abstract
Hecke has shown that the different of an extension of number fields is a square in the class group. We prove an analog for branched covers of closed -manifolds saying that the branch divisor is a square in the first homology group.
Cite
@article{arxiv.2206.00530,
title = {Hecke's Theorem on the Different for $3$-Manifolds},
author = {Will Sawin and Mark Shusterman},
journal= {arXiv preprint arXiv:2206.00530},
year = {2022}
}