Let G be a connected complex semisimple Lie group, Γ cocompact, irreducible and torsionless lattice in K maximal compact subgroup of G. Assume acts by left multiplication right on MΓ=Γ﹨G, X=G/K XΓ=Γ﹨X. In this article we prove that for any n≥0, the composition Hn(XΓ,C)→Hn(MΓ,C)→Hn(MΓ,OMΓ) is an isomorphism. As application when simply connected, compute Picard group MΓ cases rank(G) =1,2. More p...

We calculate the integrated trace anomaly for a real spin-0 scalar field in six dimensions in a torsionless curved space without a boundary. We use a path integral approach for a corresponding supersymmetric quantum mechanical model. Weyl ordering the corresponding Hamiltonian in phase space, an extra two-loop counterterm 1 8 (

We introduce a very natural class of potential submanifolds in pseudo-Euclidean spaces (each Ndimensional potential submanifold is a special flat torsionless submanifold in a 2N-dimensional pseudoEuclidean space) and prove that each N-dimensional Frobenius manifold can be locally represented as an N-dimensional potential submanifold. We show that all potential submanifolds bear natural special ...