2013/09/02 by Alain Connes, Connes, Alain, Caterina Consani +1
Mathematics · #03G30 #18B25 #19D55 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #math.AG #math.AT #msc:03G30 #msc:18B25 #msc:19D55
paper · pdf · doi:10.48550/arxiv.1309.0394
24 pages, 1 Figure
arxiv created 2013/09/02 · arxiv updated 2013/09/03
Given a point p of the topos of simplicial sets and the corresponding flat covariant functor F from the small category Delta to the category of sets, we determine the extensions of F to the cyclic category. We show that to each such cyclic structure on a point p of the topos of simplicial sets corresponds a group G(p), that such groups can be noncommutative and that each G(p) is described as the quotient of a left-ordered group by the subgroup generated by a central element. Moreover for any cyclic set X, the fiber (or geometric realization) of the underlying simplicial set of X at p inherits canonically the structure of a G(p)-space. This gives a far reaching generalization of the well-known circle action on the geometric realization of cyclic sets.