Lattices in R2 and finite subsets of a circle
Abstract
An elementary geometric construction is used to relate the space of lattices in a plane to the space exp3(S1) 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 exp3(S1) is homeomorphic to a 3-sphere and a theorem of Shchepin which says that points of exp3(S1) that correspond to one-point subsets form a trefoil knot in this 3-sphere.
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