Ailsa Keating
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View article: Symplectomorphisms and spherical objects in the conifold smoothing
Symplectomorphisms and spherical objects in the conifold smoothing Open
Let $X$ denote the ‘conifold smoothing’, the symplectic Weinstein manifold which is the complement of a smooth conic in $T^*S^3$ or, equivalently, the plumbing of two copies of $T^*S^3$ along a Hopf link. Let $Y$ denote the ‘conifold resol…
View article: A universal mirror to $(\mathbb{P}^2, Ω)$ as a birational object
A universal mirror to $(\mathbb{P}^2, Ω)$ as a birational object Open
We study homological mirror symmetry for $(\mathbb{P}^2, Ω)$ viewed as an object of birational geometry, with $Ω$ the standard meromorphic volume form. First, we construct universal objects on the two sides of mirror symmetry, focusing on …
View article: Symplectomorphisms and spherical objects in the conifold smoothing
Symplectomorphisms and spherical objects in the conifold smoothing Open
Let $X$ denote the `conifold smoothing', the symplectic Weinstein manifold which is the complement of a smooth conic in $T^*S^3$, or equivalently the plumbing of two copies of $T^*S^3$ along a Hopf link. Let $Y$ denote the `conifold resolu…
View article: Homological mirror symmetry for logCalabi–Yau surfaces
Homological mirror symmetry for logCalabi–Yau surfaces Open
Given a log Calabi-Yau surface $Y$ with maximal boundary $D$ and distinguished complex structure, we explain how to construct a mirror Lefschetz fibration $w: M \to \mathbb{C}$, where $M$ is a Weinstein four-manifold, such that the directe…
View article: On the order of Dehn twists
On the order of Dehn twists Open
This note records the order of a higher dimensional Dehn twist in a range of topologically significant groups.
View article: On symplectic stabilisations and mapping classes
On symplectic stabilisations and mapping classes Open
We are interested in comparing properties of symplectic mapping class groups of symplectic manifolds of dimension four or higher with properties of classical mapping class groups of surfaces. For $n \geq 2$, consider a configuration of Lag…
View article: Symplectomorphisms of some Weinstein 4-manifolds
Symplectomorphisms of some Weinstein 4-manifolds Open
Let M be a Weinstein four-manifold mirror to Y\D for (Y,D) a log Calabi--Yau surface; intuitively, this is typically the Milnor fibre of a smoothing of a cusp singularity. We introduce two families of symplectomorphisms of M: Lagrangian tr…
View article: Symplectomorphisms of exotic discs
Symplectomorphisms of exotic discs Open
We construct a symplectic structure on a disc that admits a compactly supported symplectomorphism which is not smoothly isotopic to the identity. The symplectic structure has an overtwisted concave end; the construction of the symplectomor…