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| Algebraic Geometry Seminar | |
| Topic: | Invariants of Finite Groups on Small Tensor Powers |
| Presenter: | Robert Guralnick, University of Southern California |
| Date: | Tuesday, May 13, 2003, Time: 4:30 p.m., Location: Fine Hall 322 |
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MAY 26 - MAY 30, 2003 |
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| Topology Seminar *** Please note special time *** | |
| Topic: | Manifolds with planar presentation and the width of satellite knots |
| Presenter: | Marty Scharlemann, University California at Santa Barbara |
| Date: | Thursday, May 29, 2003, Time: 1:00 p.m., Location: Fine Hall 314 |
| Abstract: | We consider compact 3-manifolds M
having a submersion h to R in which each generic point inverse is a planar
surface. The standard height function on a submanifold of the
3-sphere is a motivating example. To (M, h) we associate a
connectivity graph G. For M in the 3-sphere, G is a tree if
and only if there is a Fox re-imbedding of M which carries horizontal circles to
a complete collection of complementary meridian circles. On the other
hand, if the connectivity graph of the complement of M is a tree, then
there is a level preserving reimbedding of M so that its complement is a
connected sum of handlebodies. Corollary: The width of a satellite knot is no less than the width of its pattern knot. In particular, the width of K_1 # K_2 is no less than the maximum of the widths of K_1 and K_2. |