Fillings of unit cotangent bundles of nonorientable surfaces

Abstract

We prove that any minimal weak symplectic filling of the canonical contact structure on the unit cotangent bundle of a nonorientable closed surface other than the real projective plane is s-cobordant rel boundary to the disk cotangent bundle of the surface. If the nonorientable surface is the Klein bottle, then we show that the minimal weak symplectic filling is unique up to homeomorphism.Comment: 13 pages, 1 figur

Generalizations of planar contact manifolds to higher dimensions

“…(6) Given a symplectic filling of a contact manifold, a planar open book supporting the contact structure can be extended to a Lefschetz fibration over the symplectic filling, [39,48]. (7) The previous fact allows us to classify fillings of certain planar contact manifolds [29,34,42]. (8) Any weak symplectic filling of a planar contact manifold can be deformed into a Stein filling [39,48].…”