Algebraic & Geometric Topology

Inertia groups of high-dimensional complex projective spaces

Samik Basu and Ramesh Kasilingam

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1517454220

Digital Object Identifier
doi:10.2140/agt.2018.18.387

Mathematical Reviews number (MathSciNet)
MR3748247

Zentralblatt MATH identifier
1382.57013

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

Keywords
complex projective spaces smooth structures inertia groups concordance

Citation

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. https://projecteuclid.org/euclid.agt/1517454220


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