Classification of smooth structures on a homotopy complex projective space

Article Type

Research Article

Publication Title

Proceedings of the Indian Academy of Sciences: Mathematical Sciences

Abstract

We classify, up to diffeomorphism, all closed smooth manifolds homeomorphic to the complex projective n-space CPn, where n = 3 and 4. Let M2n be a closed smooth 2n-manifold homotopy equivalent to CPn. We show that, up to diffeomorphism, M6 has a unique differentiable structure and M8 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 N2n of CPn for n = 4,7 or 8 and six distinct differentiable structures on N10.

First Page

277

Last Page

281

DOI

10.1007/s12044-016-0269-4

Publication Date

5-1-2016

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