Inertia groups of high-dimensional complex projective spaces

Basu, Samik; Kasilingam, Ramesh

doi:10.2140/agt.2018.18.387

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Inertia groups of high-dimensional complex projective spaces

Samik Basu and Ramesh Kasilingam

Algebraic & Geometric Topology 18 (2018) 387–408

DOI: 10.2140/agt.2018.18.387

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.

Keywords

complex projective spaces, smooth structures, inertia groups, concordance

Mathematical Subject Classification 2010

Primary: 57R55, 57R60

Secondary: 55P25, 55P42

References

Publication

Received: 13 November 2016

Revised: 10 July 2017

Accepted: 17 July 2017

Published: 10 January 2018

Authors

Samik Basu
Department of Mathematical and Computational Science Indian Association for the Cultivation of Science Kolkata India

Ramesh Kasilingam
Theoretical Statistics and Mathematics Unit Indian Statistical Institute Bangalore India

Volume 18, issue 1 (2018)