Smooth approximations and their applications to homotopy types
| dc.contributor.author | Олександра Олександрівна Хохлюк, Sergiy Ivanovych Maksymenko | |
| dc.date.accessioned | 2021-03-04T13:56:16Z | |
| dc.date.available | 2021-03-04T13:56:16Z | |
| dc.date.issued | 2020 | |
| dc.description.abstract | Let $M, N$ the be smooth manifolds, $mathcal{C}^{r}(M,N)$ the space of ${C}^{r}$ maps endowed with the corresponding weak Whitney topology, and $mathcal{B} subset mathcal{C}^{r}(M,N)$ an open subset.It is proved that for $0<r<sleqinfty$ the inclusion $mathcal{B} cap mathcal{C}^{s}(M,N) subset mathcal{B}$ is a weak homotopy equivalence.It is also established a parametrized variant of such a result.In particular, it is shown that for a compact manifold $M$, the inclusion of the space of $mathcal{C}^{s}$ isotopies $eta:[0,1]times M to M$ fixed near ${0,1}times M$ into the space of loops $Omega(mathcal{D}^{r}(M), mathrm{id}_{M})$ of the group of $mathcal{C}^{r}$ diffeomorphisms of $M$ at $mathrm{id}_{M}$ is a weak homotopy equivalence. | |
| dc.identifier.issn | 2409-8906 | |
| dc.identifier.uri | https://card-file.ontu.edu.ua/handle/123456789/16668 | |
| dc.source | Proceedings of the International Geometry Center | |
| dc.title | Smooth approximations and their applications to homotopy types |