Concordance invariants from higher order covers

Details Concordance invariants from higher order covers Concordance invariants from higher order covers

2008-09-05

arxiv.org/abs/0809.1088v1

Mathematics

Geometric Topology

23 pages, 9 figures

Scientific paper

We generalize the Manolescu-Owens smooth concordance invariant delta(K) of knots K in the 3-sphere to invariants delta_{p^n}(K) obtained by considering covers of order p^n, with p prime. Our main result shows that for any odd prime p, the direct sum of delta_{p^n} as n ranges through the natural numbers, yields a homomorphism of infinite rank from the smooth concordance group to Z^\infty. 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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