Topologically slice knots with nontrivial Alexander polynomial

Matthew Hedden, Charles Livingston, Daniel Ruberman

Published 2010-01-10, updated 2011-05-07Version 3

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.