On the geometric realization and subdivisions of dihedral sets

By expressing the geometric realization of simplicial sets and cyclic sets as filtered colimits, Drinfeld proved in a substantially simplified way the fundamental facts that geometric realization preserves finite limits and that the group of orientation-preserving homeomorphisms of the interval [0,1] (resp. the circle R/Z) acts on the realization of a simplicial (resp. cyclic) set. In this paper we first review his method and then introduce an analogous expression for dihedral sets. We also see how these expressions lead to a clarified description of subdivisions of simplicial, cyclic, and dihedral sets.

Sho Saito <m09019h@math.nagoya-u.ac.jp>