Crossed Modules of Racks

Alissa Crans (MSRI)

Wednesday 13th May, 2015 16:00-17:00 Maths 516


A rack is a set equipped with two binary operations satisfying axioms that capture the essential properties of group conjugation and algebraically encode two of the three Reidemeister moves.  We will begin by generalizing Whitehe ad's notion of a crossed module of groups to that of a crossed module of rac ks.  Motivated by the relationship between crossed modules of groups and strict 2-groups, we then will investigate connections between our rack crosse d modules and categorified structures including strict 2-racks and trunk-like objec ts in the category of racks.  We will conclude by considering topological appl ications, such as fundamental racks.  This is joint work with Fri

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