Satellites of infinite rank in the smooth concordance group
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DOI: 10.1007/s00222-020-01026-w
Abstract: We conjecture that satellite operations are either constant or have infinite rank in the concordance group. We reduce this to the difficult case of winding number zero satellites, and use $SO(3)$ gauge theory to provide… read more here.
Keywords: smooth concordance; concordance; concordance group; infinite rank ... See more keywords
Linear independence of cables in the knot concordance group
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DOI: 10.1090/tran/8336
Abstract: We produce infinite families of knots $\{K^i\}_{i\geq 1}$ for which the set of cables $\{K^i_{p,1}\}_{i,p\geq 1}$ is linearly independent in the knot concordance group. We arrange that these examples lie arbitrarily deep in the solvable… read more here.
Keywords: concordance; smoothly slice; slice knots; knot concordance ... See more keywords
On independence of iterated Whitehead doubles in the knot concordance group
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DOI: 10.1142/s0218216518500037
Abstract: Let D(K) be the positively clasped untwisted Whitehead double of a knot K, and Tp,q be the (p,q) torus knot. We show that D(T2,2m+1) and D2(T 2,2m+1) are linearly independent in the smooth knot concordance… read more here.
Keywords: knot; concordance; independence iterated; knot concordance ... See more keywords