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Jen Hom (Georgia Tech), Triangle Topology Seminar
September 27, 2016 @ 2:00 pm - 4:00 pm
Pre-talk: SAS 2229 2-2:45
Title: The knot concordance group
Abstract: The set of knots in S^3 under the operation of connected sum forms a monoid. By quotienting by an equivalence relation called concordance, we obtain the knot concordance group. We will discuss ways of understanding the structure of this group and introduce some concordance invariants coming from Heegaard Floer theory.
Seminar talk: SAS 2102 3:00-4:00
Title: Knot concordance in homology spheres
Abstract: The knot concordance group C consists of knots in S^3 modulo concordance. We consider C_Z, the group of knots in homology spheres that bound homology balls modulo homology bordisms of pairs. Matsumoto asked if the natural map from C to C_Z is an isomorphism. Adam Levine answered this question in the negative by showing the map is not surjective. We show that the image of C in C_Z is of infinite index. This is joint work with Adam Levine and Tye Lidman.