Geometry of Integral Binary Hermitian Forms
Number Theory
2011-11-10 v2 Geometric Topology
Abstract
We generalize Conway's approach to integral binary quadratic forms on Q to study integral binary hermitian forms on quadratic imaginary extensions of Q. In Conway's case, an indefinite form that doesn't represent 0 determines a line ("river") in the spine T associated with SL(2,Z) in the hyperbolic plane. In our generalization, such a form determines a plane ("ocean") in Mendoza's spine associated with the corresponding Bianchi group SL(2,A) in hyperbolic 3-space.
Keywords
Cite
@article{arxiv.1104.1474,
title = {Geometry of Integral Binary Hermitian Forms},
author = {Mladen Bestvina and Gordan Savin},
journal= {arXiv preprint arXiv:1104.1474},
year = {2011}
}