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arXiv · 1001.1538

Topologically slice knots with nontrivial Alexander polynomial

Matthew Hedden·Charles Livingston·Daniel Ruberman
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Abstract

Let C_T be the subgroup of the smooth knot concordance group generated by topologically slice knots and let C_D be the subgroup generated by knots with trivial Alexander polynomial. We prove the quotient C_T/C_D is infinitely generated, and uncover similar structure in the 3-dimensional rational spin bordism group. Our methods also lead to the construction of links that are topologically, but not smoothly, concordant to boundary links.

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Matthew Hedden, Charles Livingston, Daniel Ruberman. 2011-05-07. Topologically slice knots with nontrivial Alexander polynomial. https://arxiv.org/abs/1001.1538

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