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

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

2009-07-27

arxiv.org/abs/0907.4789v2

Proc. London Math. Soc. 2010

Mathematics

Geometric Topology

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

Scientific paper

10.1112/plms/pdq020

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.

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