2-torsion in the n-solvable filtration of the knot concordance group

Abstract

In 1997 Cochran-Orr-Teichner introduced a natural filtration, called the n-solvable filtration, of the smooth knot concordance group, C. Its terms {F_n} are indexed by half integers. We show that each associated graded abelian group G_n=F_n/F_{n.5}, n>1, contains infinite linearly independent sets of elements of order 2 (this was known previously for n=0,1). Each of the representative knots is negative amphichiral, with vanishing s-invariant, tau-invariant, delta-invariants and Casson-Gordon invariants. Moreover each is smoothly slice in a rational homology 4-ball. In fact we show that there are many distinct such classes in G_n, distinguished by their classical Alexander polynomials and by the orders of elements in their higher-order Alexander modules.

40 pages, minor corrections, final version for Proc. London Math. Soc.; Proc. London Math. Soc. 2010

References in corpus (4)

• Primary decomposition and the fractal nature of knot concordance
• Knot concordance and Blanchfield duality
• Higher-order linking forms for 3-manifolds
• Concordance invariants from higher order covers

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• Higher-order signature cocycles for subgroups of mapping class groups and homology cylinders
• Splittings of von Neumann rho-invariants of knots
• A survey of the homology cobordism group
• Linear independence of cables in the knot concordance group
• Rational knot concordance and homology cobordism
• Amenable signatures, algebraic solutions, and filtrations of the knot concordance group