Calabi-Yau caps, uniruled caps and symplectic fillings

Tian Jun Li, Cheuk Yu Mak, Kouichi Yasui

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10 Scopus citations


We introduce symplectic Calabi-Yau caps to obtain new obstructions to exact fillings. In particular, they imply that any exact filling of the standard contact structure on the unit cotangent bundle of a hyperbolic surface has vanishing first Chern class and has the same integral homology and intersection form as its disk cotangent bundle. This gives evidence to a conjecture that all of its exact fillings are diffeomorphic to the disk cotangent bundle. As a result, we also obtain the first infinite family of Stein fillable contact 3-manifolds with uniform bounds on the Betti numbers of its exact fillings but admitting minimal strong fillings of arbitrarily large b2. Moreover, we introduce the notion of symplectic uniruled/adjunction caps and uniruled/ adjunction contact structures to present a unified picture to the existing finiteness results on the topological invariants of exact/strong fillings of a contact 3-manifold. As a byproduct, we find new classes of contact 3-manifolds with the finiteness properties and extend Wand's obstruction of planar contact 3-manifolds to uniruled/adjunction contact structures with complexity zero.

Original languageEnglish (US)
Pages (from-to)159-187
Number of pages29
JournalProceedings of the London Mathematical Society
Issue number1
StatePublished - 2017

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© 2017 London Mathematical Society.


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