Concordance invariants from higher order covers

2008/09/05 by Jabuka, Stanislav
#57M10 #57M25 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.0809.1088

Abstract

We generalize the Manolescu-Owens smooth concordance invariant delta(K) of knots K in the 3-sphere to invariants delta_pⁿ(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 delta_pⁿ 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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