Topologically slice knots with nontrivial Alexander polynomial

Details Topologically slice knots with nontrivial Alexander polynomial Topologically slice knots with nontrivial Alexander polynomial

2010-01-10

arxiv.org/abs/1001.1538v3

Mathematics

Geometric Topology

27 pages, 7 figures. Clarified discussion of Spinc structures; fixed some typos

Scientific paper

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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