## EVENT DETAILS AND ABSTRACT

**Geometry/Physics Seminar**
**Title:** Nonorientable slice genus can be arbitrarily large

**Speaker:** Josh Batson

**Speaker Info:** MIT

**Brief Description:**

**Special Note**:

**Abstract:**

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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