Abstract
We prove some contact analogs of smooth embedding theorems for closed \(\pi \)-manifolds. We show that a closed, k-connected, \(\pi \)-manifold of dimension \((2n+1)\) that bounds a \(\pi \)-manifold, contact embeds in the \((4n-2k+3)\)-dimensional Euclidean space with the standard contact structure. We also prove some isocontact embedding results for \(\pi \)-manifolds and parallelizable manifolds.
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Acknowledgements
The author is grateful to Dishant M Pancholi for his help and support during this work. He would like to thank Suhas Pandit for reading the first draft of this paper and for his helpful comments. He also thanks John Etnyre for clarifying some doubts regarding the proof of Theorem 1.25 in [10]. Finally, he thanks the referee for various comments and suggestions which helped improve the article. The author is supported by the National Board of Higher Mathematics, DAE, Government of India.
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Saha, K. Contact and isocontact embedding of \({\varvec{\pi }}\)-manifolds. Proc Math Sci 130, 52 (2020). https://doi.org/10.1007/s12044-020-00574-8
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DOI: https://doi.org/10.1007/s12044-020-00574-8