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Non-simplicity of Isocontact Embeddings in All Higher Dimensions


In this article we show that in any dimension there exist infinitely many pairs of formally contact isotopic isocontact embeddings into the standard contact sphere which are not contact isotopic. This is the first example of rigidity for contact submanifolds in higher dimensions. The contact embeddings are constructed via contact push-offs of higher-dimensional Legendrian submanifolds, a construction that generalizes the union of the positive and negative transverse push-offs of a Legendrian knot to higher dimensions.

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We are thankful to the referee for their detailed report. We are also grateful to them for suggesting the current argument for Lemma 3.4. We are grateful to Jo Nelson and Jeremy Van Horn Morris for useful discussions. R. Casals is supported by the NSF Grant DMS-1841913 and a BBVA Research Fellowship. J. Etnyre is partially supported by the NSF Grant DMS-1608684.

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Casals, R., Etnyre, J.B. Non-simplicity of Isocontact Embeddings in All Higher Dimensions. Geom. Funct. Anal. 30, 1–33 (2020).

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Mathematics Subject Classification

  • Primary 53D10
  • Secondary 53D15
  • 57R17