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On the Upsilon invariant and satellite knots

Feller, P., Park, J., & Ray, A. (2019). On the Upsilon invariant and satellite knots. Mathematische Zeitschrift, 292(3-4), 1431-1452. doi:10.1007/s00209-018-2145-7.

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arXiv:1604.04901.pdf (Preprint), 268KB
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Feller-Park-Ray_On the Upsilon invariant and satellite knots_2019.pdf (Publisher version), 607KB

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https://doi.org/10.1007/s00209-018-2145-7 (Publisher version)
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Creators:
Feller, Peter, Author
Park, JungHwan, Author
Ray, Arunima1, Author
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201

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Free keywords: Mathematics, Geometric Topology
Abstract: 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 $\{D_{2^i,1}\}_{i=1}^\infty$ 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.

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Language(s): eng - English
Dates: 2019
Publication Status: Published in print
Pages: 22
Publishing info: -
Rev. Type: Peer
Identifiers: arXiv: 1604.04901
URI: http://arxiv.org/abs/1604.04901
DOI: 10.1007/s00209-018-2145-7
Degree: -

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Title: Mathematische Zeitschrift
Abbreviation : Math. Z.
Source Genre: Journal
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Publ. Info: Springer
Pages: - Volume / Issue: 292 (3-4) Sequence Number: - Start / End Page: 1431 - 1452 Identifier: -