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Knot concordance in homology spheres

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HTLW02 - 3-manifold workshop

The knot concordance group C consists of knots in S3 modulo knots that bound smooth disks in B4. 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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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