## Finite subset spaces of the circle and a theorem of Bott

- Date: 11/15/2006

Lecturer(s):

Simon Rose (University of British Columbia)

Location:

University of British Columbia

Topic:

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