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- W1520521735 abstract "The main goal of this article is to obtain a condition under which an infinite collection $mathscr{F}$ of satellite knots (with companion a positive torus knot and pattern similar to the Whitehead link) freely generates a subgroup of infinite rank in the smooth concordance group. This goal is attained by examining both the instanton moduli space over a 4-manifold with tubular ends and the corresponding Chern-Simons invariant of the adequate 3-dimensional portion of the 4-manifold. More specifically, the result is derived from Furuta's criterion for the independence of Seifert fibred homology spheres in the homology cobordism group of oriented homology 3-spheres. Indeed, we first associate to $mathscr{F}$ the corresponding collection of 2-fold covers of the 3-sphere branched over the elements of $mathscr{F}$ and then introduce definite cobordisms from the aforementioned covers of the satellites to a number of Seifert fibered homology spheres. This allows us to apply Furuta's criterion and thus obtain a condition that guarantees the independence of the family $mathscr{F}$ in the smooth concordance group." @default.
- W1520521735 created "2016-06-24" @default.
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- W1520521735 date "2017-08-31" @default.
- W1520521735 modified "2023-09-23" @default.
- W1520521735 title "Independence of satellites of torus knots in the smooth concordance group" @default.
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- W1520521735 doi "https://doi.org/10.2140/gt.2017.21.3191" @default.
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