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Knot concordance in homology spheres

Presented by: 
Jen Hom Georgia Institute of Technology
Friday 3rd February 2017 - 11:30 to 12:30
INI Seminar Room 1
The knot concordance group C consists of knots in S^3 modulo knots that bound smooth disks in B^4. We consider C_Z, the group of knots in homology spheres that bound homology balls modulo knots that bound smooth disks in a homology ball. 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.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons