arXiv subjects

Dominique Rathel-Fournier

Publications and source records attributed to Dominique Rathel-Fournier.

2 recordsLinked to original sources

arXiv2024

Unobstructed Lagrangian cobordism groups of surfaces

We study Lagrangian cobordism groups of closed symplectic surfaces of genus $g \geq 2$ whose relations are given by unobstructed, immersed Lagrangian cobordisms. Building upon work of Abouzaid and Perrier, we compute these cobordism groups and show that they are isomorphic to the Grothendieck group of the derived Fukaya category of the surface. The proofs rely on techniques from two-dimensional topology to construct cobordisms that do not bound certain types of holomorphic polygons.

math.SG↗

arXiv2024

On cobordism groups of Lagrangian immersions

We compute the cobordism group $Ω^{\operatorname{lag}}(M)$ of Lagrangian immersions into a symplectic manifold $(M, ω)$ in terms of a stable homotopy group of a Thom spectrum constructed from $M$. This generalizes a result of Eliashberg in the case of exact symplectic manifolds. As applications, we compute $Ω^{\operatorname{lag}}(M)$ when $M$ is a closed surface and give a partial description of $Ω^{\operatorname{lag}}(M)$ when $M$ is a monotone manifold.

math.SG↗