Exactly fillable contact structures without Stein fillings
We give examples of contact structures which admit exact symplectic fillings, but no Stein fillings, answering a question of Ghiggini.
math.GT↗
arXiv subjects
Jonathan Bowden
Publications and source records attributed to Jonathan Bowden.
On foliated characteristic classes of transversally symplectic foliations
Kotschick and Morita recently discovered factorisations of characteristic classes of transversally symplectic foliations that yield new characteristic classes in foliated cohomology. We describe an alternative construction of such factorisations and construct examples of topologically trivial foliated vector bundles for which these characteristic classes are non-trivial. This shows that the foliated cohomology classes of Kotschick and Morita carry information that is not merely topological.
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On closed leaves of foliations, multisections and stable commutator lengths
We give examples of foliations that answer two questions posed by Mitsumatsu and Vogt about the genus minimising properties of closed leaves of 2-dimensional foliations on 4-manifolds. By studying stable commutator lengths in certain stable mapping class groups, we also answer an asymptotic version of another question of theirs concerning bounds on self-intersection numbers of multisections in surface bundles.
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Flat structures on surface bundles
We show that there exist flat surface bundles with closed leaves having non-trivial normal bundles. This leads us to compute the Abelianisation of surface diffeomorphism groups with marked points. We also extend a formula of Tsuboi that expresses the Euler class of a flat circle bundle in terms of the Calabi invariant of certain Hamiltonian diffeomorphisms to surfaces of higher genus and derive a similar formula for the first MMM-class of surface bundles with punctured fibre.
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The homology of surface diffeomorphism groups and a question of Morita
We answer a question posed by Morita concerning the non-triviality of certain secondary characteristic classes for surface bundles. In doing so we are naturally led to show that a form of Harer stability holds for surface diffeomorphism groups in homology of small degree.
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The topology of symplectic circle bundles
We consider circle bundles over compact three-manifolds with symplectic total spaces. We show that the base of such a space must be irreducible or the product of the two-sphere with the circle. We then deduce that such a bundle admits a symplectic form if and only if it admits one that is invariant under the circle action in three special cases: namely if the base is Seifert fibered, has vanishing Thurston norm, or if the total space admits a Lefschetz fibration.
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