Cup products and group extensions

Note on Cup-products

Skew Products in the Centralizer of Compact Abelian Group Extensions

If Tψ is an ergodic group extension of a weakly mixing transformation T having minimal self-joinings, then it is shown that isomorphism between Tψ and its inverse implies isomorphism between T and T−1. However, if T satisfies the weaker condition of being simple it is shown that that isomorphism between Tψ and its inverse does not imply the isomorphism between T and T−1. This answers a question...

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...

Group Actions and Group Extensions

In this paper we study finite group extensions represented by special cohomology classes. As an application, we obtain some restrictions on finite groups which can act freely on a product of spheres or on a product of real projective spaces. In particular, we prove that if (Z/p)r acts freely on (S1)k , then r ≤ k.

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.