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RESEARCH BLOG 3/25/03 Last week, I went to the Spring Topology and Dynamical Systems
 

Summary: RESEARCH BLOG 3/25/03
Last week, I went to the Spring Topology and Dynamical Systems
Conference at Texas Tech. There were many excellent talks. I'll
mention some that I found interesting, but see the abstracts at the
above link for a more complete picture of what talks were given.
Paul Fabel solved a problem of Dehornoy . Dehornoy showed
that the braid groups Bn are left ordered, that is they have a total
ordering which is invariant under left multiplication, and this ordering
is compatible with the embedding Bn Bn+1 by adding an n + 1st
strand. So one gets an ordering on B. Fabel put a metric on the braid
group, which enabled him to embed B into a complete topological
group B . If one takes a closed disk, and a sequence of points
converging to the boundary, then the group B is the isotopy classes
of homeomorphisms preserving these points, endowed with something
like a Lipschitz metric. Fabel shows that this completion B admits
a left ordering inducing the left order on B, answering a question of
Dehornoy .
Jennifer Schultens, in joint work with Richard Weidmann , showed
that for any N, there are graph 3-manifolds M with Heegaard genus
N+ rank(1(M)). There are examples of small Seifert fibered spaces

  

Source: Agol, Ian - Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago

 

Collections: Mathematics