SmoothInvariantsFinal.pdf (297.67 kB)
0/0

Smooth invariants of focus-focus singularities and obstructions to product decomposition

Download (297.67 kB)
journal contribution
posted on 10.09.2018 by Alexey Bolsinov, Anton Izosimov
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.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Journal of Symplectic Geometry

Volume

17

Issue

6

Pages

1613 - 1648

Citation

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 Press

Version

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

07/08/2018

Publication date

2020-01-17

ISSN

1527-5256

Language

en

Exports

Logo branding

Keyword(s)

Exports