Date: Friday 2 March 2012, 4:30pm
Location: Hempfield High School, Room 213
 Speaker: Michael McCooey, Franklin & Marshall College
   Title: Orientability of fixed-point sets of group actions on four-manifolds

Abstract.  When a cyclic group acts on a closed four-manifold,
preserving orientation, its fixed-point set is a collection of surfaces
and isolated points. Usually the surfaces are orientable---but not
always. We review what is known about necessary conditions for
orientability, and construct some explicit examples to develop a feel
for the subject.
 
If instead the group in question is Z_2 x Z_2 (a case of particular
interest to me), then the surfaces in the singular set come equipped
themselves with some additional symmetry. We examine the consequences of
this symmetry and pose a key question.
 
This will be a user-friendly talk, leading up to a discussion of work in
progress.