Smooth structures on a fake real projective space

Article Type

Research Article

Publication Title

Topology and its Applications

Abstract

We show that the group of smooth homotopy 7-spheres acts freely on the set of smooth manifold structures on a topological manifold M which is homotopy equivalent to the real projective 7-space. We classify, up to diffeomorphism, all closed manifolds homeomorphic to the real projective 7-space. We also show that M has, up to diffeomorphism, exactly 28 distinct differentiable structures with the same underlying PL structure of M and 56 distinct differentiable structures with the same underlying topological structure of M.

First Page

1

Last Page

7

DOI

10.1016/j.topol.2016.03.027

Publication Date

6-15-2016

Comments

Open Access; Bronze Open Access

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