About the College
Mathematics Colloquium: Slice Knots and the Alexander Polynomial
November 05 at 5:00 PM to 6:00 PMUngar Room 402
Mathematics Lecture
Dr. Daniel Ruberman
Brandeis University
will present
Slice Knots and the Alexander Polynomial
Thursday, November 5, 2009, 5:00pm
Ungar Room 402
Refreshments at 4:30pm in Ungar Room 521
All interested persons are welcome to attend.
Abstract: A knot in the 3-sphere is slice if it bounds an embedded disk in the 4-ball. The disk may be topologically embedded, or we may require the stronger condition that it be smoothly embedded; the knot is said to be (respectively) topologically or smoothly slice. It has been known since the early 1980's that there are knots that are topologically slice, but not smoothly slice. These result from Freedman's proof that knots with trivial Alexander polynomial are topologically slice, combined with gauge-theory techniques originating with Donaldson. In joint work with C. Livingston and M. Hedden, we answer the natural question of whether Freedman's result is responsible for all topologically slice knots. We show that the group of topologically slice knots, modulo those with trivial Alexander polynomial, is infinitely generated. The proof uses Heegaard-Floer theory.
Brandeis University
will present
Slice Knots and the Alexander Polynomial
Thursday, November 5, 2009, 5:00pm
Ungar Room 402
Refreshments at 4:30pm in Ungar Room 521
All interested persons are welcome to attend.
Abstract: A knot in the 3-sphere is slice if it bounds an embedded disk in the 4-ball. The disk may be topologically embedded, or we may require the stronger condition that it be smoothly embedded; the knot is said to be (respectively) topologically or smoothly slice. It has been known since the early 1980's that there are knots that are topologically slice, but not smoothly slice. These result from Freedman's proof that knots with trivial Alexander polynomial are topologically slice, combined with gauge-theory techniques originating with Donaldson. In joint work with C. Livingston and M. Hedden, we answer the natural question of whether Freedman's result is responsible for all topologically slice knots. We show that the group of topologically slice knots, modulo those with trivial Alexander polynomial, is infinitely generated. The proof uses Heegaard-Floer theory.
