Multivalued sections and self-maps of sphere bundles
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2022
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909189932056576 |
|---|---|
| author | Crabb, M. C. |
| author_facet | Crabb, M. C. |
| contents | Let $G$ be a finite group and $V$ a finite dimensional (non-zero) orthogonal $G$-module such that, for each prime $p$ dividing the order of $G$, the subspace of $V$ fixed by a Sylow $p$-subgroup of $G$ is non-zero and, if the dimension of $V$ is odd, has dimension greater than $1$. Using ideas of Avvakumov, Karasev, Kudrya and Skopenkov and work of Noakes on self-maps of sphere bundles, we show that, for any principal $G$-bundle $P\to X$ over a compact ENR $X$, there exists a $G$-map from $P$ to the unit sphere $S(V)$ in $V$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_09637 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Multivalued sections and self-maps of sphere bundles Crabb, M. C. Algebraic Topology 55M25, 55M35, 55R25, 55P69, 55S40, 57S17 Let $G$ be a finite group and $V$ a finite dimensional (non-zero) orthogonal $G$-module such that, for each prime $p$ dividing the order of $G$, the subspace of $V$ fixed by a Sylow $p$-subgroup of $G$ is non-zero and, if the dimension of $V$ is odd, has dimension greater than $1$. Using ideas of Avvakumov, Karasev, Kudrya and Skopenkov and work of Noakes on self-maps of sphere bundles, we show that, for any principal $G$-bundle $P\to X$ over a compact ENR $X$, there exists a $G$-map from $P$ to the unit sphere $S(V)$ in $V$. |
| title | Multivalued sections and self-maps of sphere bundles |
| topic | Algebraic Topology 55M25, 55M35, 55R25, 55P69, 55S40, 57S17 |
| url | https://arxiv.org/abs/2208.09637 |