3:00 p.m., Friday (October 24, 2003)
Math Annex 1100
Certain dynamics on 3-manifolds and embedding open 3-manifolds into 3-space
Motivated by Morse theory and Smale's work in dynamics, as well
as our study of cheirality, the following questions are studied and
answered, in joint work with Boju Jiang and Yi Ni:
(1) When does a 3-manifold admit an automorphism having a knotted
Smale solenoid as attractor?
(2) When does a 3-manifold admit an automorphism whose non-wandering
set consists of Smale solenoids?
The result presents some intrinsic symmetries for a class of
Furthermore, the simplest example in (2) involves the discovery of a
non-fibred knot whose infinite cyclic covering embeds into the 3-sphere.
The existence of such an example was asked by Stallings and Edwards 20
We also give some obstruction to embedding the infinite cyclic coverings
of compact 3-manifolds into compact 3-manifolds.
Refreshments will be served at 2:45 p.m. in the Faculty Lounge,
Math Annex (Room 1115).