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Comparing minimal simplicial models

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Adamaszek, Michał (2013) Comparing minimal simplicial models. Journal of Homotopy and Related Structures, Volume 8 (Number 1). pp. 117-125. doi:10.1007/s40062-012-0014-3

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Official URL: http://dx.doi.org/10.1007/s40062-012-0014-3

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Abstract

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 T 0-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.

Item Type: Journal Article
Divisions: Faculty of Science > Mathematics
Journal or Publication Title: Journal of Homotopy and Related Structures
Publisher: Springer
ISSN: 2193-8407
Official Date: 2013
Dates:
DateEvent
2013Published
Volume: Volume 8
Number: Number 1
Page Range: pp. 117-125
DOI: 10.1007/s40062-012-0014-3
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access

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