• Classification of smooth structures on a homotopy complex projective space

• Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/126/02/0277-0281

• Keywords

Complex projective spaces; smooth structures; inertia groups; concordance.

• Abstract

We classify, up to diffeomorphism, all closed smooth manifolds homeomorphic to the complex projective $n$-space ${\mathbb C}{\bf P}^n$, where $n = 3$ and 4. Let $M^{2n}$ be a closed smooth $2n$-manifold homotopy equivalent to ${\mathbb C}{\bf P}^n$. We show that, up to diffeomorphism, $M^6$ has a unique differentiable structure and $M^8$ has at most two distinct differentiable structures. We also show that, up to concordance, there exist at least two distinct differentiable structures on a finite sheeted cover $N^2n$ of ${\mathbb C}{\bf P}^n$ for $n = 4, 7 {\rm or} 8$ and six distinct differentiable structures on $N^{10}$.

• Proceedings – Mathematical Sciences

Volume 130, 2020
All articles
Continuous Article Publishing mode

• Editorial Note on Continuous Article Publication

Posted on July 25, 2019