A symplectic isotopy of a Dehn twist on CPn x CPn+1

• Autores: Emiko Dupont
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 80, Nº 1, 2009, págs. 171-190
• Idioma: inglés
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• Resumen

  • The complex manifold CPn �~ CPn+1 with symplectic form �Ð�Ê = �ÐCPn + �Ê�ÐCPn+1, where �ÐCPn and �ÐCPn+1 are normalized Fubini.Study forms, n �¸ N and �Ê > 1 a real number, contains a natural Lagrangian sphere L�Ê. We prove that the Dehn twist along L�Ê is symplectically isotopic to the identity for all �Ê > 1. This isotopy can be chosen so that it pointwise fixes a complex hypersurface in CPn �~ CPn+1 and lifts to the blow-up of CPn �~ CPn+1 along a complex n-dimensional submanifold.