TY - THES
AU - Rose, Simon
PY - 2007
TI - Finite subset spaces of the circle
KW - Thesis/Dissertation
LA - eng
M3 - Text
AB - 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theorem of Bott and a newer (unpublished) result of E .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.
N2 - 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theorem of Bott and a newer (unpublished) result of E .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.
UR - https://open.library.ubc.ca/collections/831/items/1.0080474
ER - End of Reference