This article is cited in 1 paper

Vanishing cycles in complex symplectic geometry

M. D. Garay<sup>ab

a</sup> Institut des Hautes Études Scientifiques
^b Johannes Gutenberg – Universität Mainz, Institut für Mathematik

Abstract: We study the vanishing cycles on the Milnor fibre for some non-isolated singularities which appear naturally in symplectic geometry. Under assumptions given in the text, we show that the vanishing cycles associated to a distinguished basis freely generate the corresponding homology groups of the Milnor fibre. We derive some consequences of this fact, in particular for the study of integrable systems and of adjoint orbits in Lie algebras.

Key words and phrases: Monodromy, vanishing cycles, integrable systems, symplectic geometry, lagrangian varieties, involutive varieties, simple Lie algebras.

MSC: 32S50

Received: October 19, 2006

Language: English

DOI: 10.17323/1609-4514-2008-8-1-73-90

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