Nonlocal loss of first homotopy in polyhedral approximations of Peano continua
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918340836982784 |
|---|---|
| author | Brazas, Jeremy Fischer, Hanspeter |
| author_facet | Brazas, Jeremy Fischer, Hanspeter |
| contents | If a Peano continuum $X$ is semilocally simply connected, then it has a finite polyhedral approximation whose fundamental group is isomorphic to that of $X$. In general, this fails to be true. It is known that the fundamental group of a locally complicated Peano continuum may contain nontrivial elements that are persistently undetectable by polyhedral approximations, at all scales. However, we show that such failure is not inherently local. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_01041 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonlocal loss of first homotopy in polyhedral approximations of Peano continua Brazas, Jeremy Fischer, Hanspeter Algebraic Topology 55Q52, 55Q07 (Primary) 55Q05, 54F50 (Secondary) If a Peano continuum $X$ is semilocally simply connected, then it has a finite polyhedral approximation whose fundamental group is isomorphic to that of $X$. In general, this fails to be true. It is known that the fundamental group of a locally complicated Peano continuum may contain nontrivial elements that are persistently undetectable by polyhedral approximations, at all scales. However, we show that such failure is not inherently local. |
| title | Nonlocal loss of first homotopy in polyhedral approximations of Peano continua |
| topic | Algebraic Topology 55Q52, 55Q07 (Primary) 55Q05, 54F50 (Secondary) |
| url | https://arxiv.org/abs/2508.01041 |