Geometry/Physics Seminar

Title: Nonorientable slice genus can be arbitrarily large
Speaker: Josh Batson
Speaker Info: MIT
Brief Description:
Special Note:

The cross-section of a surface smoothly embedded in four-space is a knot or a link. Every knot can be realized as the cross-section of *some* surface, but if that surface is required to be orientable, then work of Milnor, Fox, and Murasugi show that its genus may need to be quite large. For example, the (2,n) torus knot formed by braiding two strands is not a cross-section of any orientable surface with genus less than n-1, but is the cross-section of Klein bottle. Using a combination of classical algebraic topology, four-dimensional surgery, and Heegaard-Floer homology, we show that the (2k+2, 2k+1) torus knot is not a cross-section of *any* smoothly embedded surface in four-space with first betti number less than 2k.
Date: Tuesday, March 19, 2013
Time: 4:00pm
Where: Lunt 107
Contact Person: Michael Couch
Contact email: mcouch@math.northwestern.edu
Contact Phone:
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