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Smooth and topological concordance of satellites of torus knots

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Speaker: 
Paul Kirk
Affiliation: 
Indiana U, Bloomington/MPIM
Date: 
Thu, 12/11/2015 - 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

Two knots in the 3-sphere are called concordant if they cobound an annulus in the cylinder. The resulting equivalence classes form a group called the concordance group. There are several variants, the smooth (i.e. C^infty), the topological (i.e C^0) and the algebraic (which classifies concordance in dimensions>4) concordance groups. I'll describe and outline the proofs of two results concerning satellites of knots obtained as links of algebraic singularities. First, that the Whitehead doubles of torus knots span a infinite rank subgroup of the smooth concordance group which lies in the kernel of the forgetful map to the topological concordance group. Second, that a subgroup of the topological concordance group spanned by links of algebraic singularities form an infinite rank subgroup which lies in the kernel of the map to the algebraic concordance group.

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