Free subgroup of the $C^0$ symplectic mapping class group
Alexandre Jannaud
TL;DR
This paper extends a result to $C^0$ symplectic topology showing that Dehn twists about certain Lagrangian spheres generate a free subgroup of the $C^0$ symplectic mapping class group, using barcode technology and continuity results.
Contribution
It introduces a novel extension of Keating's result to $C^0$ symplectic topology, demonstrating the freeness of Dehn twists subgroup under specific conditions.
Findings
Dehn twists about Lagrangian spheres generate a free subgroup
Extension of Keating's result to $C^0$ symplectic topology
Use of barcode technology and continuity results
Abstract
Using the technology of barcodes and previously proven continuity results, we extend to symplectic topology a beautiful result from Keating. Given two Lagrangian spheres in a Liouville domain, with good conditions, we prove that the Dehn twists about these spheres generate a free subgroup of the symplectic mapping class group.
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Taxonomy
TopicsGeometric and Algebraic Topology · Geometry and complex manifolds · Homotopy and Cohomology in Algebraic Topology