Unknotting Numbers and Knot Floer Homology Jonathan Johnson, Oklahoma State University Host: Jonathan Johnson This will be an introductory talk that gives background for next week's colloquium talk.
Abstract: The unknotting number is a very natural and classical invariant of a knot. Despite this, this invariant is not well understood. For example, it is an open question how unknotting numbers behave under basic knot operations such as the connect sum and satellite operations. Floer homology has provide a suite of new invariants for 3-maifolds which has provided new techniques to study classical problems in knot theory. In preparation for next week's colloquium talk by Jennifer Hom, we will define knot Floer homology and discuss how it has been used to study unknotting numbers.
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