Maksim Maydanskiy

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Lefschetz fibrations provide one of the available methods for constructing symplectic structures. This paper builds on the model of [13], where that method was used to find a non-standard counterpart to the symplectic manifold obtained by attaching an n-handle to the cotangent bundle of the (n + 1)-sphere (for any even n ≥ 2). Here, we explore a somewhat(More)
In this thesis I construct, in all odd complex dimensions, pairs of Liouville domains W0 and W1 which are diffeomorphic to the cotangent bundle of the sphere with one extra subcritical handle, but are not symplectomorphic. While W0 is symplectically very similar to the cotangent bundle itself, W1 is more unusual. I use Seidel’s exact triangles for Floer(More)
In the proof of [4, Lemma 1.1], we appealed to an explicit isotopy of totally real spheres, constructed in [3, Section 5]. That construction works in the lowest dimension (n = 2), but is wrong in general (one of the endpoints is not the desired sphere). Here, we explain a different approach, leading to a corrected version of [4, Lemma 1.1], which requires(More)
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