On the integral cohomology of quotients of manifolds by cyclic groups

Grégoire Menet (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

We propose new tools based on basic lattice theory to calculate the integral cohomology of the quotient of a manifold by an automorphism group of prime order. As examples of applications, we provide the Beauville--Bogomolov forms of some irreducible symplectic orbifolds; we also show a new expression for a basis of the integral cohomology of a Hilbert scheme of two points on a surface.

Mots clés: Group actions on lattices; Compact orientable manifolds; Beauville–Bogomolov forms; Integral cohomology

Domaines: Géométrie algébrique [math.AG]

Grégoire Menet. On the integral cohomology of quotients of manifolds by cyclic groups. Journal de Mathématiques Pures et Appliquées, 2018, 119, pp.280-325. ⟨10.1016/j.matpur.2017.11.008⟩. ⟨hal-01701004⟩