Algebraic & Geometric Topology

Inertia groups of high-dimensional complex projective spaces

Samik Basu and Ramesh Kasilingam

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For a complex projective space the inertia group, the homotopy inertia group and the concordance inertia group are isomorphic. In complex dimension 4 n + 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.

Article information

Algebr. Geom. Topol., Volume 18, Number 1 (2018), 387-408.

Received: 13 November 2016
Revised: 10 July 2017
Accepted: 17 July 2017
First available in Project Euclid: 1 February 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R55: Differentiable structures 57R60: Homotopy spheres, Poincaré conjecture
Secondary: 55P25: Spanier-Whitehead duality 55P42: Stable homotopy theory, spectra

complex projective spaces smooth structures inertia groups concordance


Basu, Samik; Kasilingam, Ramesh. Inertia groups of high-dimensional complex projective spaces. Algebr. Geom. Topol. 18 (2018), no. 1, 387--408. doi:10.2140/agt.2018.18.387.

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