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- W2963273600 abstract "Abstract We show that generically a pseudogroup generated by holomorphic diffeomorphisms defined about $0in mathbb{C} $ is free in the sense of pseudogroups even if the class of conjugacy of the generators is fixed. This result has a number of consequences on the topology of leaves for a (singular) holomorphic foliation defined on a neighborhood of an invariant curve. In particular, in the classical and simplest case arising from local nilpotent foliations possessing a unique separatrix which is given by a cusp of the form ${ {y}^{2} - {x}^{2n+ 1} = 0} $ , our results allow us to settle the problem of showing that a generic foliation possesses only countably many non-simply connected leaves." @default.
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- W2963273600 date "2013-07-01" @default.
- W2963273600 modified "2023-09-27" @default.
- W2963273600 title "Generic pseudogroups on and the topology of leaves" @default.
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- W2963273600 doi "https://doi.org/10.1112/s0010437x13007161" @default.
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