#### Volume 18, issue 1 (2018)

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Inertia groups of high-dimensional complex projective spaces

### Samik Basu and Ramesh Kasilingam

Algebraic & Geometric Topology 18 (2018) 387–408
##### Abstract

For a complex projective space the inertia group, the homotopy inertia group and the concordance inertia group are isomorphic. In complex dimension $4n+1$, these groups are related to computations in stable cohomotopy. Using stable homotopy theory, we make explicit computations to show that the inertia group is nontrivial in many cases. In complex dimension $9$, we deduce some results on geometric structures on homotopy complex projective spaces and complex hyperbolic manifolds.

##### Keywords
complex projective spaces, smooth structures, inertia groups, concordance
##### Mathematical Subject Classification 2010
Primary: 57R55, 57R60
Secondary: 55P25, 55P42