Geodesic
On the geometric realization and subdivisions of dihedral sets
Saito, Sho1
1Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya 464-8602, Japan
Algebraic and Geometric Topology, Tome 13 (2013) no. 2, pp. 1071-1087
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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.

DOI : 10.2140/agt.2013.13.1071
Classification : 18G30, 55U10
Keywords: geometric realization, dihedral set, subdivision

Saito, Sho  1

1 Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya 464-8602, Japan 
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Saito, Sho. On the geometric realization and subdivisions of dihedral sets. Algebraic and Geometric Topology, Tome 13 (2013) no. 2, pp. 1071-1087. doi: 10.2140/agt.2013.13.1071

[1] M Bökstedt, W C Hsiang, I Madsen, The cyclotomic trace and algebraic $K$-theory of spaces, Invent. Math. 111 (1993) 465

[2] V Drinfeld, On the notion of geometric realization, Mosc. Math. J. 4 (2004) 619, 782

[3] Z Fiedorowicz, J L Loday, Crossed simplicial groups and their associated homology, Trans. Amer. Math. Soc. 326 (1991) 57

[4] J Milnor, The geometric realization of a semi-simplicial complex, Ann. of Math. 65 (1957) 357

[5] G Segal, Configuration-spaces and iterated loop-spaces, Invent. Math. 21 (1973) 213

[6] J Spaliński, Homotopy theory of dihedral and quaternionic sets, Topology 39 (2000) 557

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