Finite subset spaces of the circle and a theorem of Bott

  • Date: 11/15/2006

Simon Rose (University of British Columbia)


University of British Columbia


By considering the circle as the boundary of the hyperbolic plane we
are able to describe the first three unordered configuration spaces of
the circle by considering them as particular quotients of the group of
isometries of the hyperbolic plane. After determining how these join
together and calculating their fundamental group, we describe their
union exp_3(S1) as a simply connected Seifert-Fibred space, hence S3.
Moreover, a slight variation of this method reveals that the inclusion
of S1 into this space is in fact the trefoil knot.

Other Information: 

Algebraic Topology Seminar 2006