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Iso-contact embeddings of manifolds in co-dimension 2
Date Issued
01-01-2022
Author(s)
Pancholi, Dishant M.
Indian Institute of Technology, Madras
Abstract
The purpose of this article is to study co-dimension 2 iso-contact embeddings of closed contact manifolds. We first show that a closed contact manifold (M2n−1, ξM) iso-contact embeds in a contact manifold (N2n+1, ξN), provided M contact embeds in (N, ξN) with trivial normal bundle and the contact structure induced on M via this embedding is overtwisted and homotopic as an almost-contact structure to ξM. We apply this result to show that a closed contact 3–manifold having no 2–torsion in its second integral cohomology iso-contact embeds in the standard contact 5–sphere if and only if the first Chern class of the contact structure is zero. Finally, we discuss iso-contact embeddings of closed simply connected contact 5–manifolds.
Volume
20