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Inertia groups and smooth structures on quaternionic projective spaces

Inertia groups and smooth structures on quaternionic projective spaces AbstractThis paper deals with certain results on the number of smooth structures on quaternionic projective spaces, obtained through the computation of inertia groups and their analogues, which in turn are computed using techniques from stable homotopy theory. We show that the concordance inertia group is trivial in dimension 20, but there are many examples in high dimensions where the concordance inertia group is non-trivial. We extend these to computations of concordance classes of smooth structures. These have applications to 3-sphere actions on homotopy spheres and tangential homotopy structures. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

Inertia groups and smooth structures on quaternionic projective spaces

Forum Mathematicum , Volume 34 (2): 15 – Mar 1, 2022

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References (53)

Publisher
de Gruyter
Copyright
© 2022 Walter de Gruyter GmbH, Berlin/Boston
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/forum-2020-0125
Publisher site
See Article on Publisher Site

Abstract

AbstractThis paper deals with certain results on the number of smooth structures on quaternionic projective spaces, obtained through the computation of inertia groups and their analogues, which in turn are computed using techniques from stable homotopy theory. We show that the concordance inertia group is trivial in dimension 20, but there are many examples in high dimensions where the concordance inertia group is non-trivial. We extend these to computations of concordance classes of smooth structures. These have applications to 3-sphere actions on homotopy spheres and tangential homotopy structures.

Journal

Forum Mathematicumde Gruyter

Published: Mar 1, 2022

Keywords: Quaternionic projective spaces; smooth structures; concordance; 57R60; 57R55; 55P42; 55P25

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