Date
Mon, 27 May 2024
14:15
Location
L4
Speaker
Abigail Ward
Organisation
Cambridge

The relationship between the topological or homotopy-invariant properties of a symplectic manifold X and the set of possible immersed or embedded Lagrangian submanifolds of X is rich and mostly mysterious.  In 2020, D. Alvarez-Gavela, Y. Eliashberg, and D. Nadler proved that any Weinstein manifold (e.g. an affine variety) admitting a Lagrangian plane field retracts onto a Lagrangian submanifold with arboreal singularities (a certain class of singularities which can be described combinatorially). I will discuss work in progress with D. Alvarez-Gavela and T. Large investigating the other direction, in which we prove a partial converse to the AGEN result and show that most Weinstein manifolds do not admit such skeleta. This suggests that the Floer-theoretic invariants of some well-known open symplectic manifolds may be more complicated than expected.

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