Lattices in R^2 and finite subsets of a circle
Geometric Topology
2007-05-23 v2 General Topology
Abstract
An elementary geometric construction is used to relate the space of lattices in a plane to the space exp_3(S^1) of the subsets of a circle of cardinality at most 3. As a consequence we obtain new proofs of a theorem of Bott which says that exp_3(S^1) is homeomorphic to a 3-sphere and a theorem of Shchepin which says that points of exp_3(S^1) that correspond to one-point subsets form a trefoil knot in this 3-sphere.
Cite
@article{arxiv.math/9911224,
title = {Lattices in R^2 and finite subsets of a circle},
author = {Jacob Mostovoy},
journal= {arXiv preprint arXiv:math/9911224},
year = {2007}
}
Comments
2 pages, 1 figure; a minor error corrected