Commutators and cup products

Note on Cup-products

Square-free words as products of commutators

Elements of the commutator subgroup of a free group F can be presented as values of canonical forms, called Wicks forms. We show that, starting from sufficiently high genus g, there is a sequence of words wg which can be presented by f .g/ distinct Wicks forms, where f .g/ > gŠ. Moreover we may choose these words wg to be square-free. Mathematics Subject Classification (2000). 20E05, 20F10.

Powers of Commutators as Products of Squares

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...

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.