Journal of Differential Geometry

Non-isotopic Legendrian submanifolds in R2n+1

Tobias Ekholm, John Etnyre, and Michael Sullivan

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In the standard contact (2n + 1)-space when n > 1, we construct infinite families of pairwise non-Legendrian isotopic, Legendrian n-spheres, n-tori and surfaces which are indistinguishable using classically known invariants. When n is even, these are the first known examples of non-Legendrian isotopic, Legendrian submanifolds of (2n + 1)-space. Such constructions indicate a rich theory of Legendrian submanifolds. To distinguish our examples, we compute their contact homology which was rigorously defined in this situation in [7].

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J. Differential Geom., Volume 71, Number 1 (2005), 85-128.

First available in Project Euclid: 29 March 2006

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Ekholm, Tobias; Etnyre, John; Sullivan, Michael. Non-isotopic Legendrian submanifolds in R 2n+1. J. Differential Geom. 71 (2005), no. 1, 85--128. doi:10.4310/jdg/1143644313.

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