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Exact Lagrangian immersions with one double point revisited
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2014 (English)In: Mathematische Annalen, ISSN 0025-5831, E-ISSN 1432-1807, Vol. 358, no 1-2, 195-240 p.Article in journal (Refereed) Published
Abstract [en]

We study exact Lagrangian immersions with one double point of a closed orientable manifold into . We prove that if the Maslov grading of the double point does not equal then is homotopy equivalent to the sphere, and if, in addition, the Lagrangian Gauss map of the immersion is stably homotopic to that of the Whitney immersion, then bounds a parallelizable -manifold. The hypothesis on the Gauss map always holds when or when . The argument studies a filling of obtained from solutions to perturbed Cauchy-Riemann equations with boundary on the image of the immersion. This leads to a new and simplified proof of some of the main results of Ekholm and Smith (Exact Lagrangian immersions with a single double point 2011)). which treated Lagrangian immersions in the case by applying similar techniques to a Lagrange surgery of the immersion, as well as to an extension of these results to the odd-dimensional case.

Place, publisher, year, edition, pages
2014. Vol. 358, no 1-2, 195-240 p.
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URN: urn:nbn:se:uu:diva-220803DOI: 10.1007/s00208-013-0958-6ISI: 000330830400007OAI: oai:DiVA.org:uu-220803DiVA: diva2:706718
Available from: 2014-03-21 Created: 2014-03-20 Last updated: 2014-03-21Bibliographically approved

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