Topology Seminar: Orderings, eigenvalues and surgery

  • Date: 02/09/2010
Dale Rolfsen (UBC)

University of British Columbia


In joint work with Adam Clay, we establish a necessary condition that an automorphism of an orderable group can preserve an ordering: at least one of its eigenvalues, suitably defined, must be real and positive. Applications will be given to knot theory and to the fundamental groups of fibred spaces. An example: if surgery on a fibred knot in $S^3$ (or in a homology 3-sphere) produces a 3-manifold whose fundamental group is orderable, then the surgery must be longitudinal (0-framed) and the Alexander polynomial of the knot must have a positive real root.


3:00pm - 4:00pm, WMAX 216.