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- W2398210258 abstract "We study two homomorphisms to the rational homology sphere group. If $psi$ denotes the inclusion homomorphism from the integral homology sphere group, then using work of Lisca we show that the image of $psi$ intersects trivially with the subgroup of the rational homology sphere group generated by lens spaces. As corollaries this gives a new proof that the cokernel of $psi$ is infinitely generated, and implies that a connected sum $K$ of 2-bridge knots is concordant to a knot with determinant 1 if and only if $K$ is smoothly slice. Furthermore, if $beta$ denotes the homomorphism from the knot concordance group defined by taking double branched covers of knots, we prove that the kernel of $beta$ contains a $mathbb{Z}^{infty}$ summand by analyzing the Tristram-Levine signatures of a family of knots whose double branched covers all bound rational homology balls." @default.
- W2398210258 created "2016-06-24" @default.
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- W2398210258 date "2016-05-25" @default.
- W2398210258 modified "2023-09-27" @default.
- W2398210258 title "Knot concordance and homology sphere groups" @default.
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