Kaydedildi:
| Asıl Yazarlar: | , |
|---|---|
| Materyal Türü: | Preprint |
| Baskı/Yayın Bilgisi: |
2020
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| Konular: | |
| Online Erişim: | https://arxiv.org/abs/2012.05378 |
| Etiketler: |
Etiketle
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İçindekiler:
- We develop a theory of $\times$-homotopy, fundamental groupoids and covering spaces that apply to non-simple graphs, generalizing existing results for simple graphs. We prove that $\times$-homotopies from finite graphs can be decomposed into moves which adjust at most one vertex at a time, generalizing the spider lemma of \cite{CS1}. We define a notion of homotopy covering map and develop a theory of universal covers and deck transformations, generalizing \cites{TardifWroncha, Matsushita} to non-simple graphs. We examine the case of reflexive graphs, where each vertex has at least one loop. We also prove that these homotopy covering maps satisfy a homotopy lifting property for arbitrary graph homomorphisms, generalizing path lifting results of \cites{Matsushita, TardifWroncha}.