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Finite subset spaces of the circle Rose, Simon

Abstract

In this thesis we investigate a new and highly geometric approach to studying finite subset spaces of the circle. By considering the circle as the boundary of the hyperbolic plane, we are able to use the full force of hyperbolic geometry—in particular, its well-understood group of isometries—to determine explicitely the structure of the first few configuration spaces of the circle S¹. Once these are understood we then move onto studying their union—that is, exp₃(S¹,)—and in particular, we re-prove both an old theorem of Bott and a newer (unpublished) result of E . Щепин (E. Shchepin) about this space.

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