CSU HAYWARD

DEPARTMENT OF MATHEMATICS AND

COMPUTER SCIENCE

COLLOQUIUM

Friday, May 31, 2002; Noon-1pm Sc N321

Speaker: Karen Edwards, UC Berkeley and Diablo Valley College

Heegaard Splittings, or, How to Get a Handle on Understanding 3-manifolds

Years ago people believed the earth was flat, and we laugh in retrospect at their naivete. Yet today, not one of us knows the shape of the universe we live in. The topological answer to that puzzle lies somewhere in the world of 3 and 4 dimensional manifolds. Mathematically, the classification of 3-manifolds is still an unsolved problem, but even more immediate is the question: How on earth can you picture a 3-manifold?

This talk will focus on the visualization of 3-manifolds using a structure called Heegaard splittings. (Every closed 3-manifold has a Heegaard splitting, which means it can be formed by gluing together two multiple-holed donuts, known as "handlebodies".) By the end of this talk you will be able to move around in the 3-manifold of your choice. In addition, results on the classification of 3-manifolds, the theory of Heegaard splittings, and the current NASA space probe mission to discover the topology of the universe will be covered as desired by the audience.

 

Please join us beforehand for pizza.