Tori in four-dimensional Milnor fibres

Ailsa Keating (Massachusetts Institute of Technology)

Monday 13th January, 2014 16:00-17:00 Maths 204


The Milnor fibre of any isolated hypersurface singularity contains exact
Lagrangian spheres: the vanishing cycles associated to a Morsification of
the singularity. Moreover, for simple singularities, it is known that the
only possible exact Lagrangians are spheres. I will explain how to
construct exact Lagrangian tori in the Milnor fibres of all non-simple
singularities of real dimension four. Time allowing, I will use these to
give examples of fibres whose Fukaya categories are not generated by
vanishing cycles. 

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