Geodesic
Framed bordism and Lagrangian embeddings of exotic spheres
Mohammed Abouzaid1
1 Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307
Annals of mathematics, Tome 175 (2012) no. 1, pp. 71-185.

Voir la notice de l'article provenant de la source Annals of Mathematics website

In dimensions congruent to 1 modulo 4, we prove that the cotangent bundle of an exotic sphere which does not bound a parallelisable manifold is not symplectomorphic to the cotangent bundle of the standard sphere. More precisely, we prove that such an exotic sphere cannot embed as a Lagrangian in the cotangent bundle of the standard sphere. The main ingredients of the construction are (1) the fact that the graph of the Hopf fibration embeds the standard sphere, and hence any Lagrangian which embeds in its cotangent bundle, as a displaceable Lagrangian in the product a symplectic vector space of the appropriate dimension with its complex projective space, and (2) a moduli space of solutions to a perturbed Cauchy-Riemann equation introduced by Gromov.
DOI : 10.4007/annals.2012.175.1.4

Mohammed Abouzaid 1

1 Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307 
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Mohammed Abouzaid. Framed bordism and Lagrangian embeddings  of exotic spheres. Annals of mathematics, Tome 175 (2012) no. 1, pp. 71-185. doi : 10.4007/annals.2012.175.1.4. https://geodesic-test.mathdoc.fr/articles/10.4007/annals.2012.175.1.4/

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