Farrell–Jones spheres and
inertia groups of complex projective spaces

Kasilingam Ramesh

doi:10.1515/forum-2013-0072

Published by De Gruyter January 10, 2014

Farrell–Jones spheres and inertia groups of complex projective spaces

Kasilingam Ramesh

From the journal Forum Mathematicum

https://doi.org/10.1515/forum-2013-0072

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Abstract

We introduce and study a new class of homotopy spheres called Farrell–Jones spheres. Using Farrell–Jones sphere we construct examples of closed negatively curved manifolds M2n, where n = 7 or 8, which are homeomorphic but not diffeomorphic to complex hyperbolic manifolds, thereby giving a partial answer to a question raised by C. S. Aravinda and F. T. Farrell. We show that every exotic sphere not bounding a spin manifold (Hitchin sphere) is a Farrell–Jones sphere. We also discuss the relationship between inertia groups of ℂℙn and Farrell–Jones spheres.

Keywords: Locally symmetric space; exotic smooth structure; complex hyperbolic; inertia groups

MSC: 57R60; 57C24; 57R55; 53C56

The author would like to thank Professor F. T. Farrell for initiating him into the beautiful area of mathematics. The author would also like to thank his advisor, Professor A. R. Shastri, for continual encouragement and many useful comments. Finally, the author thanks the referee for his suggestions toward the improved presentation of this paper.

Received: 2013-5-8

Revised: 2013-10-18

Published Online: 2014-1-10

Published in Print: 2015-9-1

Farrell–Jones spheres and inertia groups of complex projective spaces

Abstract

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