Continued fractions and Einstein manifolds of infinite topological type
Differential Geometry
2007-05-23 v1
Abstract
We present a construction of complete self-dual Einstein metrics of negative scalar curvature on an uncountable family of manifolds of infinite topological type, which are enumerated by continued fraction expansions of irrational numbers. These manifolds may be regarded as limits of the resolutions of cyclic quotient singularities (governed by continued fraction expansions of rational numbers) on which we constructed complete self-dual Einstein metrics in previous work.
Cite
@article{arxiv.math/0508614,
title = {Continued fractions and Einstein manifolds of infinite topological type},
author = {David M. J. Calderbank and Michael A. Singer},
journal= {arXiv preprint arXiv:math/0508614},
year = {2007}
}
Comments
16 pages; 1 figure