Transfinite product reduction in fundamental groupoids
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2020
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866929685072445440 |
|---|---|
| author | Brazas, Jeremy |
| author_facet | Brazas, Jeremy |
| contents | Infinite products, indexed by countably infinite linear orders, arise naturally in the context of fundamental groupoids. Such products are called "transfinite" if the index orders are permitted to contain a dense suborder and are called "scattered" otherwise. In this paper, we prove several technical lemmas related to the reduction (i.e. combining of factors) of transfinite products in fundamental groupoids. Applying these results, we show that if the transfinite fundamental group operations are well-defined in a space $X$ with a scattered algebraic $1$-wild set $\mathbf{aw}(X)$, then all transfinite fundamental groupoid operations are also well-defined. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2001_06733 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Transfinite product reduction in fundamental groupoids Brazas, Jeremy Algebraic Topology General Topology 57M05, 55Q52, 08A65 Infinite products, indexed by countably infinite linear orders, arise naturally in the context of fundamental groupoids. Such products are called "transfinite" if the index orders are permitted to contain a dense suborder and are called "scattered" otherwise. In this paper, we prove several technical lemmas related to the reduction (i.e. combining of factors) of transfinite products in fundamental groupoids. Applying these results, we show that if the transfinite fundamental group operations are well-defined in a space $X$ with a scattered algebraic $1$-wild set $\mathbf{aw}(X)$, then all transfinite fundamental groupoid operations are also well-defined. |
| title | Transfinite product reduction in fundamental groupoids |
| topic | Algebraic Topology General Topology 57M05, 55Q52, 08A65 |
| url | https://arxiv.org/abs/2001.06733 |