Free subgroup of the $C^0$ symplectic mapping class group

Using the technology of barcodes and previously proven continuity results, we extend to $C^0$ 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 $C^0$ symplectic mapping class group.