On the Upsilon invariant and satellite knots

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We study the effect of satellite operations on the Upsilon invariant of Ozsvath-Stipsicz-Szabo. We obtain results concerning when a knot and its satellites are independent; for example, we show that the set {D2i,1}i=1 infinity is a basis for an infinite rank summand of the group of smooth concordance classes of topologically slice knots, for D the positive clasped untwisted Whitehead double of any knot with positive tau-invariant, e.g. the right-handed trefoil. We also prove that the image of the Mazur satellite operator on the smooth knot concordance group contains an infinite rank subgroup of topologically slice knots.
Publisher
SPRINGER HEIDELBERG
Issue Date
2019-08
Language
English
Article Type
Article
Citation

MATHEMATISCHE ZEITSCHRIFT, v.292, no.3-4, pp.1431 - 1452

ISSN
0025-5874
DOI
10.1007/s00209-018-2145-7
URI
http://hdl.handle.net/10203/280199
Appears in Collection
MA-Journal Papers(저널논문)
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