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Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/34775

Title: Smooth invariants of focus-focus singularities and obstructions to product decomposition
Authors: Bolsinov, Alexey V.
Izosimov, Anton
Issue Date: 2018
Publisher: International Press
Citation: BOLSINOV, A.V. and IZOSIMOV, A., 2018. Smooth invariants of focus-focus singularities and obstructions to product decomposition. Journal of Symplectic Geometry, In Press.
Abstract: We 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.
Description: This paper is in closed access until it is published.
Version: Accepted for publication
URI: https://dspace.lboro.ac.uk/2134/34775
Publisher Link: http://www.intlpress.com/site/pub/pages/journals/items/jsg/_home/_main/index.html
ISSN: 1527-5256
Appears in Collections:Closed Access (Maths)

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1706.07456.pdfSubmitted version282.49 kBAdobe PDFView/Open
SmoothInvariantsFinal.pdfAccepted version297.67 kBAdobe PDFView/Open


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