Legendrian satellites

John Etnyre; Vera Vértesi

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arXiv · 1608.05695

Legendrian satellites

John Etnyre·Vera Vértesi

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Abstract

In this paper we study Legendrian knots in the knot types of satellite knots. In particular, we classify Legendrian Whitehead patterns and learn a great deal about Legendrian braided patterns. We also show how the classification of Legendrian patterns can lead to a classification of the associated satellite knots if the companion knot is Legendrian simple and uniformly thick. This leads to new Legendrian and transverse classification results for knots in the 3-sphere with its standard contact structure as well as a more general perspective on some previous classification results.

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John Etnyre, Vera Vértesi. 2016-08-19. Legendrian satellites. https://arxiv.org/abs/1608.05695

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