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Professor Qiu Rui-Feng, Dalian University of Technology

Thursday, 2-4pm, July 14, 2005.

 (1) Operations of Heegaard splittings
 
 abstract: Connected sum, boundary connected sum, self-boundary connected sum and amagalmation are basic methods to construct any 3-manifolds from irreducible, boundary irreducible, small 3-manifolds. Corresponding to the above operations of 3-manifolds, there are the same operations of Heegaard splittings. In this talk, we shall introduce some recently results on the operations of Heegaard splittings.
 
 (2) Unknotting number one knots are prime.

 abstract: There is an old conjecture in knot theory, that says, the unknotting number of a composite knot is the sum of unknotting numbers of its two factors. Martin Scharlrmann proved that unknotting number one knots are prime. This is only one result on unknotting number conjecture. In this talk, we shall introduce a simple combinatorial method to prove Martin Scharlrmann's result.