 
Summary: RESEARCH BLOG 4/8/03: EFFICIENT CELL STRUCTURES ON
3MANIFOLDS
Wednesday, I am heading to Fayetteville, Arkansas, for the Spring
Lecture Series in Mathematical Sciences, which is being well organized
by Yo'av Rieck. The principal speaker will be Andrew Casson, who
will be speaking on the AndrewsCurtis and the Poincare conjectures.
Dave Fisher was at Yale last year, and his office was next to Casson's
office. He said Casson was filling his blackboard with group presenta
tions, apparently in an effort to understand the AndrewsCurtis conjec
ture. Since Casson does much of his work on his chalkboard, including
preparing his lectures in complete detail ahead of time, we decided that
someone should put in a "Casson cam" in Casson's office, which would
take a snapshot of his blackboard periodically so his work could be
preserved for posterity. Unfortunately, Casson is not in the habit of
writing his work up, even though it is usually of very high quality, so
many people try to glean some understanding of what he is working on
from his lectures.
Jaco and Rubinstein have introduced the notion of an efficient tri
angulation of a 3manifold [4]. They show that for an irreducible M3
,
