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
Abstract

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.

Keywords
geometric realization, dihedral set, subdivision
Mathematical Subject Classification 2010
Primary: 18G30
Secondary: 55U10
References
Publication
Received: 19 August 2012
Revised: 4 December 2012
Accepted: 19 December 2012
Published: 17 April 2013
Authors
Sho Saito
Graduate School of Mathematics
Nagoya University
Furocho
Chikusaku
Nagoya 464-8602
Japan
http://www.math.nagoya-u.ac.jp/~m09019h/