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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
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: |
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| 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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