Concordance invariants from higher order covers
Abstract
We generalize the Manolescu-Owens smooth concordance invariant delta(K) of knots K in the 3-sphere to invariants deltapn(K) obtained by considering covers of order pn, with p prime. Our main result shows that for any odd prime p, the direct sum of deltapn as n ranges through the natural numbers, yields a homomorphism of infinite rank from the smooth concordance group to Z∞. We also show that unlike delta, these new invariants typically are not multiples of the knot signature, even for alternating knots. A significant portion of the article is devoted to exploring examples.
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