Volume 13, issue 2 (2013)

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On the geometric realization and subdivisions of dihedral sets

Sho Saito

Algebraic & Geometric Topology 13 (2013) 1071–1087

We extend to dihedral sets Drinfeld’s filtered-colimit expressions of the geometric realization of simplicial and cyclic sets. We prove that the group of homeomorphisms of the circle continuously act on the geometric realization of a dihedral set. We also see how these expressions of geometric realization clarify subdivision operations on simplicial, cyclic and dihedral sets defined by Bökstedt, Hsiang and Madsen, and Spaliński.

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geometric realization, dihedral set, subdivision
Mathematical Subject Classification 2010
Primary: 18G30
Secondary: 55U10
Received: 19 August 2012
Revised: 4 December 2012
Accepted: 19 December 2012
Published: 17 April 2013
Sho Saito
Graduate School of Mathematics
Nagoya University
Nagoya 464-8602