Smooth structures on $\mathbb{C}P^{m}$ for $5\leq m\leq 8$
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2017
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909005252657152 |
|---|---|
| author | Kasilingam, Ramesh |
| author_facet | Kasilingam, Ramesh |
| contents | We classify up to diffeomorphism all smooth manifolds homeomorphic to the complex projective m-space $\mathbb{C}P^{m}$ for $m = 5, 6, 7$ and $8$. As an application, for $m = 7$ and $8$, we compute the smooth tangential structure set of $\mathbb{C}P^{m}$ and obtain a bound on the number of smooth homotopy complex projective m-spaces with given Pontryagin classes up to orientation-preserving diffeomorphism. We also show that there exists a smooth manifold which is tangentially homotopy equivalent but not homeomorphic to $\mathbb{C}P^{8}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1701_07592 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Smooth structures on $\mathbb{C}P^{m}$ for $5\leq m\leq 8$ Kasilingam, Ramesh Geometric Topology 57R55, 55P42, 57R60, 57R67 We classify up to diffeomorphism all smooth manifolds homeomorphic to the complex projective m-space $\mathbb{C}P^{m}$ for $m = 5, 6, 7$ and $8$. As an application, for $m = 7$ and $8$, we compute the smooth tangential structure set of $\mathbb{C}P^{m}$ and obtain a bound on the number of smooth homotopy complex projective m-spaces with given Pontryagin classes up to orientation-preserving diffeomorphism. We also show that there exists a smooth manifold which is tangentially homotopy equivalent but not homeomorphic to $\mathbb{C}P^{8}$. |
| title | Smooth structures on $\mathbb{C}P^{m}$ for $5\leq m\leq 8$ |
| topic | Geometric Topology 57R55, 55P42, 57R60, 57R67 |
| url | https://arxiv.org/abs/1701.07592 |