Spectral sequences arising from the gauge equation

Michel Boyom (1) , Stephane Puechmorel (2)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 OPTIM - ENAC - Equipe Optim

The gauge equation is a generalization of the conjugacy relation for Koszul connection to 1 bundle morphisms that are not isomorphisms. The existence of non-trivial solution to this equation, 2 especially when duality is imposed upon related connections, gives important information about the 3 geometry of the manifolds considered. In this article, we use the gauge equation to introduce spectral 4 sequences that are further specialized to Hessian structures. 5

Mots clés: Gauge equation; spectral sequence; KV-cohomology; hessian manifold; statistical manifold

Domaines: Mathématiques [math]

Michel Boyom, Stephane Puechmorel. Spectral sequences arising from the gauge equation. 2024. ⟨hal-04514836⟩