TL;DR
This paper demonstrates that all right-angled Artin groups can be embedded into the group of Hamiltonian symplectomorphisms of the 2-sphere, revealing a deep connection between algebraic and symplectic structures.
Contribution
It establishes the first embedding of arbitrary RAAGs into the symplectic group of the 2-sphere, linking combinatorial group theory with symplectic geometry.
Findings
Every RAAG embeds in the Hamiltonian symplectomorphism group of the 2-sphere.
The result bridges algebraic and geometric structures in symplectic topology.
Provides new tools for understanding the algebraic structure of symplectomorphism groups.
Abstract
We prove that every RAAG (a Right-Angled Artin Group) embeds in the group of Hamiltonian symplectomorphisms of the 2-sphere.
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Taxonomy
TopicsVeterinary Equine Medical Research