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Pulling back the Gromoll-Meyer construction and models of exotic spheres


Author: L. D. Sperança
Journal: Proc. Amer. Math. Soc. 144 (2016), 3181-3196
MSC (2010): Primary 57R60, 57R50
DOI: https://doi.org/10.1090/proc/12945
Published electronically: October 22, 2015
MathSciNet review: 3487247
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Abstract: The Gromoll-Meyer construction of an exotic 7-sphere is generalized by producing geometric models of exotic 8-, 10- and Kervaire spheres as quotients of principal bundles over spheres. Also, using the geometry of their geodesics, the group structure of homotopy 8-spheres is explicitly presented.


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Additional Information

L. D. Sperança
Affiliation: Departamento de Matemática, UFPR, Setor de Ciências Exatas, Centro Politécnico, Caixa Postal 019081, CEP 81531-990, Curitiba, PR, Brazil
Email: lsperanca@ufpr.br

DOI: https://doi.org/10.1090/proc/12945
Received by editor(s): May 29, 2014
Received by editor(s) in revised form: August 23, 2014, March 26, 2015, and September 1, 2015
Published electronically: October 22, 2015
Additional Notes: The author was financially supported by FAPESP, grant numbers 2009/07953-8 and 2012/25409-6.
Communicated by: Guofang Wei
Article copyright: © Copyright 2015 American Mathematical Society

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