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# Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964

Mathematical Citation Quotient (MCQ) 2018: 0.71

Online
ISSN
1435-5337
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Volume 27, Issue 5

# Farrell–Jones spheres and inertia groups of complex projective spaces

Kasilingam Ramesh
Published Online: 2014-01-10 | DOI: https://doi.org/10.1515/forum-2013-0072

## 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 ${M}^{2n}$, 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 $ℂ{ℙ}^{n}$ and Farrell–Jones spheres.

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

Revised: 2013-10-18

Published Online: 2014-01-10

Published in Print: 2015-09-01

Citation Information: Forum Mathematicum, Volume 27, Issue 5, Pages 3005–3015, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741,

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