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Cascade Topology Seminar


Prof. Martin Scharlemann
Mathematics Department
Univ. of California @ Santa Barbara
Santa Barbara, CA 93106  USA

Title:  Generating the genus g+1 Goeritz group of a genus g handlebody 

Abstract:  A specific set of 4g+1 elements is shown to generate the Goeritz group of the genus g+1 Heegaard splitting of a genus g handlebody.  These generators are consistent with Powell's proposed generating set for the Goeritz group of the genus g+1 splitting of the 3-sphre.  There are two proofs: one using purely classical techniques and one using thin position.  I hope to be able to at least sketch both proofs.


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