Gysin sequences and cohomology ring of symplectic fillings

Gysin sequences and cohomology ring of symplectic fillings

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Zhengyi Zhou, IAS
IAS - West Building Lecture Hall

It is conjectured that contact manifolds admitting flexible fillings have unique exact fillings. In this talk, I will show that exact fillings (with vanishing first Chern class) of a flexibly fillable contact (2n-1)-manifold share the same product structure on cohomology if one of the multipliers is of even degree smaller than n-1. The main argument uses Gysin sequences from symplectic cohomology twisted by sphere bundles.