2134/34775
Alexey Bolsinov
Alexey
Bolsinov
Anton Izosimov
Anton
Izosimov
Smooth invariants of focus-focus singularities and obstructions to product decomposition
Loughborough University
2018
untagged
Mathematical Sciences not elsewhere classified
2018-09-10 10:02:30
Journal contribution
https://repository.lboro.ac.uk/articles/journal_contribution/Smooth_invariants_of_focus-focus_singularities_and_obstructions_to_product_decomposition/9376784
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.