Open AccessPulling back the Gromoll-Meyer construction and models of exotic spheres
Author(s) -
Llohann D. Sperança
Publication year - 2015
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/proc/12945
Subject(s) - spheres , geodesic , mathematics , bott periodicity theorem , principal (computer security) , homotopy , quotient , separate spheres , pure mathematics , mathematical analysis , homotopy sphere , homotopy group , computer science , physics , political science , astronomy , law , operating system , ideology , politics
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.