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Smooth invariants of focus-focus singularities and obstructions to product decomposition
journal contribution
posted on 2018-09-10, 10:02 authored by Alexey BolsinovAlexey Bolsinov, Anton IzosimovWe study focus-focus singularities (also known as nodal singularities, or pinched tori)
of Lagrangian fibrations on symplectic 4-manifolds. We show that, in contrast to elliptic and hyperbolic singularities, there exist homeomorphic focus-focus singularities which are not diffeomorphic. Furthermore, we obtain an algebraic description of the moduli space of focus-focus singularities up to smooth equivalence, and show that for double pinched
tori this space is one-dimensional. Finally, we apply our construction to disprove Zung’s
conjecture which says that any non-degenerate singularity can be smoothly decomposed into an almost direct product of standard singularities.
History
School
- Science
Department
- Mathematical Sciences
Published in
Journal of Symplectic GeometryVolume
17Issue
6Pages
1613 - 1648Citation
BOLSINOV, A.V. and IZOSIMOV, A., 2019. Smooth invariants of focus-focus singularities and obstructions to product decomposition. Journal of Symplectic Geometry, 17 (6), pp.1613-1648.Publisher
International PressVersion
- AM (Accepted Manuscript)
Publisher statement
This paper was accepted for publication in the journal Journal of Symplectic Geometry and the definitive published version is available at https://dx.doi.org/10.4310/JSG.2019.v17.n6.a2.Acceptance date
2018-08-07Publication date
2020-01-17ISSN
1527-5256eISSN
1540-2347Publisher version
Language
- en