• Classification of smooth structures on a homotopy complex projective space

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      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 $N^{10}$.

    • Author Affiliations

       
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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      Posted on July 25, 2019

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