Volume 18, issue 1 (2018)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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
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