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Length and the Gromov Norm of a 3-manifold
Geometry/Topology| Speaker: | Chris Jerdonek, Mathematics, UC Davis |
| Location: | 693 Kerr |
| Start time: | Wed, Nov 17 1999, 4:10PM |
Description
Gromov defined a topological invariant that is proportional to the
volume for hyperbolic 3-manifolds. Parallel to this I will introduce
a topological measure of the length of an isotopy class of curves
in a 3-manifold that is proportional to the length for geodesics in a
hyperbolic manifold. This allows a topological characterization of the
isotopy class of a geodesic in a hyperbolic 3-manifold. In particular,
the length is defined for 3-manifolds that a priori are not known to
have hyperbolic structures. This could provide therefore a missing
step in the cone-manifold program. It may not be too difficult to
verify, for closed manifolds with positive Gromov norm, the basic
properties of the length function needed for this step to proceed.
And curiously, it is not obvious that the length is not meaningful
for manifolds with zero Gromov norm.