On the geometric realization and subdivisions of dihedral sets

Saito, Sho

doi:10.2140/agt.2013.13.1071

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On the geometric realization and subdivisions of dihedral sets

Sho Saito

Algebraic & Geometric Topology 13 (2013) 1071–1087

DOI: 10.2140/agt.2013.13.1071

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/

Volume 13, issue 2 (2013)