Commutative classifying space for simplicial groups
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866909981368909824 |
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| author | Okay, Cihan Zsámboki, Pál |
| author_facet | Okay, Cihan Zsámboki, Pál |
| contents | In this paper, we introduce a simplicial analog of classifying spaces for commutativity which classify principal bundles with commutativity structure on their transition functions. Our construction $\overline W(τ,K)$, which takes as input a simplicial group $K$ and a cosimplicial group $τ$ that encodes the additional structure such as commutativity, is a variation of the $\overline W$-construction for simplicial groups. Our main result shows that the geometric realization of our $\overline W(τ,K)$ is homotopy equivalent to the topological classifying space $B(τ,|K|)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2001_04052 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Commutative classifying space for simplicial groups Okay, Cihan Zsámboki, Pál Algebraic Topology In this paper, we introduce a simplicial analog of classifying spaces for commutativity which classify principal bundles with commutativity structure on their transition functions. Our construction $\overline W(τ,K)$, which takes as input a simplicial group $K$ and a cosimplicial group $τ$ that encodes the additional structure such as commutativity, is a variation of the $\overline W$-construction for simplicial groups. Our main result shows that the geometric realization of our $\overline W(τ,K)$ is homotopy equivalent to the topological classifying space $B(τ,|K|)$. |
| title | Commutative classifying space for simplicial groups |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2001.04052 |