Lattices in R^2 and finite subsets of a circle

Details Lattices in R^2 and finite subsets of a circle Lattices in R^2 and finite subsets of a circle

1999-11-27

arxiv.org/abs/math/9911224v2

Mathematics

Geometric Topology

2 pages, 1 figure; a minor error corrected

Scientific paper

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.

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