arXiv subjects

Stephane Tchuiaga

Publications and source records attributed to Stephane Tchuiaga.

3 recordsLinked to original sources

arXiv2026

Abel-Jacobi Map and Symplectic Topology

We develop a harmonic-coordinate approach to the identity component $G_\omega(\Sigma_g)$ of the symplectomorphism group of a closed oriented surface of genus $g\ge2$. Using an intrinsic decomposition of the Abel-Jacobi displacement into a global flux part and a zero-average harmonic fluctuation, we introduce the harmonic flux norm and prove its non-degeneracy on the full identity component without Floer theory. We also show the norm is continuous in the $C^0$-topology, deduce that $\mathrm{Ham}(\Sigma_g,\omega)$ is $C^0$-closed inside $G_\omega(\Sigma_g)$, and produce a locally injective harmonic-coordinate chart near the identity. Along the way we derive first-order expansions for the norm, quantitative fixed-point obstructions, and propose a finite-dimensional persistence invariant (the harmonic barcode) associated to the harmonic displacement filtration.

math.SG↗

arXiv2026

Isomorphism of cosymplectomorphism groups implies diffeomorphism of manifolds

We prove that if two closed, connected, regular cosymplectic manifolds have isomorphic groups of cosymplectomorphisms (as topological groups), then the underlying manifolds are diffeomorphic. The proof proceeds by characterizing the Reeb flow as the center of the group and descending the isomorphism to the symplectic base manifolds. We show that the isomorphism preserves the conjugacy class of the monodromy of the mapping torus, which ensures that the bundle structures, and thus the total spaces are equivalent.

math.SG↗

arXiv2024

On Banyaga's conjecture on the group of symplectic homeomorphisms

This paper addresses Banyaga's conjecture asserting that : the group of strong symplectic homeomorphisms is a proper normal subgroup of the symplectic homeomorphism group of a closed symplectic manifold.

math.SG↗