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Obstructing Sliceness in Odd Pretzel Knots
by
Kathryn Bryant
Bryn Mawr College
Coauthors: Paul Melvin
We apply techniques from Greene and Jabuka's 2011 paper on the Slice-Ribbon Conjecture for odd, 3-stranded pretzel knots to say the following: (1) All odd pretzel knots having a difference of 2 or more in the number of positive twist parameters and the number of negative twist parameters have infinite order in the smooth knot concordance group, and (2) 0-Pair, odd, 5-stranded pretzel knots are not slice.
The proofs involve the classical slice obstruction coming from the knot signature, as well as more modern slice obstructions coming from Donaldson's Diagonalization Theorem and d-invariants from Heegaard-Floer homology.
Date received: October 27, 2015
Copyright © 2015 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cblw-20.