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Article
Open AccessTrisecting a 4-dimensional book into three chapters
We describe an algorithm that takes as input an open book decomposition of a closed oriented 4-manifold and outputs an explicit trisection diagram of that 4-manifold. Moreover, a slight variation of this algor...
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Article
Stein traces and characterizing slopes
We show that there exists an infinite family of pairwise non-isotopic Legendrian knots in the standard contact 3-sphere whose Stein traces are equivalent. This is the first example of such phenomenon. Differen...
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Article
Open AccessThe Classification of Surfaces via Normal Curves
We present a simple proof of the surface classification theorem using normal curves. This proof is analogous to Kneser’s and Milnor’s proof of the existence and uniqueness of the prime decomposition of 3-manif...
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Article
Open AccessA Boothby–Wang Theorem for Besse Contact Manifolds
A Reeb flow on a contact manifold is called Besse if all its orbits are periodic, possibly with different periods. We characterize contact manifolds whose Reeb flows are Besse as principal
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Article
Symplectic dynamics and the 3-sphere
Given a knot in a closed connected orientable 3-manifold we prove that if the exterior of the knot admits an aperiodic contact form that is Euclidean near the boundary, then the 3-manifold is diffeomorphic to ...
