On the geometric realization and subdivisions of dihedral sets

Details On the geometric realization and subdivisions of dihedral sets On the geometric realization and subdivisions of dihedral sets

2010-12-02

arxiv.org/abs/1012.0380v3

Mathematics

Algebraic Topology

22 pages. A few arguments added

Scientific paper

By expressing the geometric realization of simplicial sets and cyclic sets as filtered colimits, Drinfeld (arXiv:math/0304064v3) 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 Drinfeld's method and then introduce an analogous expression for the geometric realization of dihedral sets. We also see how these expressions lead to a clarified description of subdivisions of simplicial, cyclic, and dihedral sets.

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