Journal of Homotopy and Related Structures

, Volume 8, Issue 1, pp 117–125 | Cite as

Comparing minimal simplicial models



We compare minimal combinatorial models of homotopy types: arbitrary simplicial complexes, flag complexes and order complexes. Flag complexes are the simplicial complexes which do not have the boundary of a simplex of dimension greater than one as an induced subcomplex. Order complexes are classifying spaces of posets and they correspond to models in the category of finite T0-spaces. In particular, we prove that stably, that is after a suitably large suspension, the optimal flag complex representing a homotopy type is approximately twice as big as the optimal simplicial complex with that property (in terms of the number of vertices). We also investigate some related questions.


Triangulation Simplicial complex Minimal model Homotopy type 

Mathematics Subject Classification (1991)

55P10 55U10 55P40 


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Copyright information

© Tbilisi Centre for Mathematical Sciences 2012

Authors and Affiliations

  1. 1.Mathematics Institute and DIMAPUniversity of WarwickCoventryUK

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