Splitting symplectic monodromy

2026/01/28 by Ailsa Keating, Ivan Smith, Michael Wemyss · 1 voice
Mathematics · #math.SG

paper · pdf

v2: 38p, version accepted for publication. To appear in the SIGMA Special Issue on Geometry and Dynamics in memory of Will Merry

arxiv published 2026/01/28 · arxiv created 2026/08/06 · arxiv updated 2026/08/07

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.

Citations

• Plumbings of lens spaces and crepant resolutions of compound A_n singularities
• Homological mirror symmetry for projective K3 surfaces
• The wrapped Fukaya category of plumbings
• Equivariant Fukaya categories at singular values
• Symplectomorphisms and spherical objects in the conifold smoothing
• Rabinowitz Fukaya categories and the categorical formal punctured neighborhood of infinity
• Cluster categories from Fukaya categories
• Symplectomorphisms of some Weinstein 4-manifolds
• Algebraic sheaves of Floer homology groups via algebraic torus actions on the Fukaya category
• Intrinsic mirror symmetry and categorical crepant resolutions
• The Birman-Hilden theory
• Dehn-Seidel twist, C⁰ symplectic topology and barcodes
• Double bubble plumbings and two-curve flops
• Homological mirror symmetry for log Calabi-Yau surfaces
• Stability Conditions for 3-fold Flops
• Cluster exchange groupoids and framed quadratic differentials
• Symplectic topology of K3 surfaces via mirror symmetry
• A bijection between m-cluster-tilting objects and (m+2)-angulations in m-cluster categories
• Covariantly functorial wrapped Floer theory on Liouville sectors
• A trichotomy for the autoequivalence groups on smooth projective surfaces
• Exotic spheres and the topology of symplectomorphism groups
• Contractible stability spaces and faithful braid group actions
• Decorated marked surfaces: spherical twists versus braid twists
• Picard-Lefschetz theory and dilating C^*-actions
• Quiver algebras as Fukaya categories
• Lagrangian Torus Fibrations and Homological Mirror Symmetry for the Conifold
• Quadratic differentials as stability conditions
• Exact Lagrangians in A_n-surface singularities
• Tagged mapping class groups: Auslander-Reiten translation
• Moduli of surfaces with an anti-canonical cycle
• Combinatorial rigidity of arc complexes
• Compact Moduli Spaces of Del Pezzo Surfaces and Kähler-Einstein metrics
• Relative singularity categories I: Auslander resolutions
• Exchange graphs and Ext quivers
• Abstract analogues of flux as symplectic invariants
• Exact Lagrangians in plumbings
• Lagrangian spheres, symplectic surfaces and the symplectic mapping class group
• Symplectic birational transformations of the plane
• Floer cohomology and pencils of quadrics
• On the cluster category of a marked surface without punctures
• Topological quantum field theory structure on symplectic cohomology
• Effect of Legendrian Surgery
• Symplectic mapping class groups of some Stein and rational surfaces
• Uniqueness of enhancement for triangulated categories
• Derived equivalences from mutations of quivers with potential
• Rabinowitz Floer homology and symplectic homology
• Strongly Fillable Contact Manifolds and J-holomorphic Foliations
• Cluster categories for algebras of global dimension 2 and quivers with potential
• An open string analogue of Viterbo functoriality
• Braids, mapping class groups, and categorical delooping
• A geometric description of m-cluster categories
• Symplectomorphism groups and embeddings of balls into rational ruled 4-manifolds
• Moduli of objects in dg-categories
• Moduli of objects in dg-categories
• Lectures on four-dimensional Dehn twists
• DG quotients of DG categories
• The topology of the space of symplectic balls in rational 4-manifolds
• Quivers, Floer cohomology, and braid group actions
• Graded Lagrangian submanifolds
• Graded lagrangian submanifolds
• Symplectic automorphisms of T^*S²
• Affine Artin groups and the fundamental groups of some moduli spaces
• Pseudo holomorphic curves in symplectic manifolds

Discussions

• Ailsa Keating, Ivan Smith, Michael Wemyss: Splitting symplectic monodromy https://arxiv.org/abs/2601.20438 https://arxiv.org/pdf/2601.20438 https://arxiv.org/html/2601.20438 [bsky, 0 points, 0 comments]

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