Cup products in Grassmannians

On embedded products of Grassmannians

Let Γ′ and Γ be two Grassmannians. The standard embedding φ : Γ′ × Γ→ P is obtained by combining the Plücker and Segre embeddings. Given a further embedding η : Γ′ × Γ→ P′, we find a sufficient condition for the existence of α ∈ Aut(Γ) and of a collineation ψ : P→ P′ such that η = (idΓ′ × α)φψ. A.M.S. classification number: 51M35.

Cup Products in Computational Topology

Topological persistence methods provide a robust framework for analyzing large point cloud datasets topologically, and have been applied with great success towards homology computations on simplicial complexes. In this paper, we apply the persistence algorithm towards calculating a set of invariants related to the cup product structure on the cohomology ring for a space. These invariants expres...

Note on Cup-products

Netherlands Cup products and mixed Hodge structures

Let X be a complete complex algebraic variety of dimension n and let D be a divisor with strict normal crossings on X. In this paper we show that the cup product maps i+j D (X) are morphisms of mixed Hodge structures.

Incompressibility of Products by Grassmannians of Isotropic Subspaces

We prove that the product of an arbitrary projective homogeneous variety Y by an orthogonal, symplectic, or unitary Grassmannian X is 2-incompressible if and only if the varieties XF (Y ) and YF (X) are so. Some new properties of incompressible Grassmannians are established on the way.