Colloquium
3:00 p.m., Friday (October 24, 2003)
Math Annex 1100
Shicheng Wang
Peking University
Certain dynamics on 3manifolds and embedding open 3manifolds into 3space
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 3manifold admit an automorphism having a knotted
Smale solenoid as attractor?
(2) When does a 3manifold admit an automorphism whose nonwandering
set consists of Smale solenoids?
The result presents some intrinsic symmetries for a class of
3manifolds.
Furthermore, the simplest example in (2) involves the discovery of a
nonfibred knot whose infinite cyclic covering embeds into the 3sphere.
The existence of such an example was asked by Stallings and Edwards 20
years ago.
We also give some obstruction to embedding the infinite cyclic coverings
of compact 3manifolds into compact 3manifolds.
Refreshments will be served at 2:45 p.m. in the Faculty Lounge,
Math Annex (Room 1115).
