Dear Topologists and Friends of Topology,
Trent will give the first seminar talk of the semester tomorrow
(Thursday) at 3:30 in MSCS 514. Title and abstract are below:
Title: Lower bounds on the Heegaard genus of amalgamated $3$-manifolds.
Abstract: I describe some new results of mine which place lower bounds on
the Heegaard genus of a $3$-manifold which is obtained by gluing two
$3$-manifolds together along torus boundary components. As an application,
I also put a lower bound on tunnel number degeneration under connected sum
of knots. These kinds of problem have been worked on for quite some time,
but as far as I know my techniques are new and the results are of a
different flavor.