The Szczarba map and the cubical cobar construction
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917426314084352 |
|---|---|
| author | Franz, Matthias |
| author_facet | Franz, Matthias |
| contents | We consider a twisting function from a 1-reduced simplicial set $X$ to a simplicial group $G$. We prove in detail that the associated Szczarba operators induce a simplicial map from the triangulation of the cubical cobar construction of $X$ to $G$. This confirms a result due to Minichiello-Rivera-Zeinalian and gives, as pointed out by these authors, a conceptual proof of the fact that the dga map $Ω\,C(X) \to C(G)$ induced by Szczarba's twisting cochain is comultiplicative. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01669 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Szczarba map and the cubical cobar construction Franz, Matthias Algebraic Topology 55U10 (Primary), 55P35, 57T30 (Secondary) We consider a twisting function from a 1-reduced simplicial set $X$ to a simplicial group $G$. We prove in detail that the associated Szczarba operators induce a simplicial map from the triangulation of the cubical cobar construction of $X$ to $G$. This confirms a result due to Minichiello-Rivera-Zeinalian and gives, as pointed out by these authors, a conceptual proof of the fact that the dga map $Ω\,C(X) \to C(G)$ induced by Szczarba's twisting cochain is comultiplicative. |
| title | The Szczarba map and the cubical cobar construction |
| topic | Algebraic Topology 55U10 (Primary), 55P35, 57T30 (Secondary) |
| url | https://arxiv.org/abs/2507.01669 |