Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 22 (2026), 080, 36 pages      arXiv:2601.20438      https://doi.org/10.3842/SIGMA.2026.080
Contribution to the Special Issue on Geometry and Dynamics in memory of Will Merry

Splitting Symplectic Monodromy

Ailsa Keating a, Ivan Smith a and Michael Wemyss b
a) Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, CB3 0WB, UK
b) School of Mathematics and Statistics, University of Glasgow, University Place, Glasgow G12 8QQ, UK

Received January 29, 2026, in final form August 06, 2026; Published online August 24, 2026

Abstract
We discuss some examples in which symplectic monodromy (provably or conjecturally) splits off the symplectic mapping class group, hoping to illustrate different techniques and inputs to the arguments. Along the way we formulate several open questions and conjectures. Inter alia, we also construct a compact symplectic six-manifold which contains infinitely many pairwise disjoint Lagrangian 3-spheres.

Key words: symplectic manifolds; Fukaya categories; spherical twists; homological mirror symmetry.

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