具有接触奇点的闭辛流形中Fomenko-Zieschang不变量的实现

Pub Date : 2022-01-01 DOI:10.1070/SM9579

D. B. Zot’ev, V. I. Sidel'nikov

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引用次数: 0

摘要

研究了由附加环柄引起的不变流形上的Liouville叶的拓扑分岔。证明了每个标记分子(Fomenko-Zieschang不变量)都可以在具有接触奇点的闭辛流形的不变量子流形上实现，该子流形是通过将环柄依次附加到一组辛流形上而得到的，而这些辛流形具有与原子相关的局部平凡颤振结构。参考书目:10篇。

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Realization of Fomenko-Zieschang invariants in closed symplectic manifolds with contact singularities

The topological bifurcations of Liouville foliations on invariant -manifolds that are induced by attaching toric -handles are investigated. It is shown that each marked molecule (Fomenko-Zieschang invariant) can be realized on an invariant submanifold of a closed symplectic manifold with contact singularities which is obtained by attaching toric -handles sequentially to a set of symplectic manifolds, while these latter have the structures of locally trivial fibrations over associated with atoms. Bibliography: 10 titles.

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