arXiv subjects

Julio Sampietro Christ

Publications and source records attributed to Julio Sampietro Christ.

2 recordsLinked to original sources

arXiv2025

Equivariant Lagrangian displacements

This paper proves that certain monotone Lagrangians in the standard symplectic vector space cannot be displaced by a Hamiltonian isotopy which commutes with the antipodal map. The method of proof is to develop a Borel equivariant version of the quantum cohomology of Biran and Cornea, and prove it is sensitive to equivariant displacements. The Floer--Euler class of Biran and Khanevsky appears as a term in the equivariant differential in certain cases.

math.SG↗

arXiv2025

Equivariant Floer homology is isomorphic to reduced Floer homology

Given a symplectic manifold equipped with a Hamiltonian $G$-action and two $G$-invariant Lagrangians, we lift the construction of equivariant Lagrangian Floer homology of G.\@~Cazassus to the Novikov ring by constructing a ``quantum'' model in the vein of Biran and Cornea and Schmäschke. Using this refinement, we prove Cazassus' conjecture that, if the action on the zero-level of the moment map is free, then equivariant Floer homology agrees with the Floer homology of the Marsden-Weinstein reduction.

math.SG↗