Pulling back the Gromoll-Meyer construction and models of exotic spheres
Llohann D. Speran\c{c}a
TL;DR
This paper generalizes the Gromoll-Meyer construction to produce geometric models of various exotic spheres, including 8, 10, and Kervaire spheres, as quotients of sphere bundles over spheres.
Contribution
It introduces new geometric models of exotic spheres as quotients of sphere bundles, extending the Gromoll-Meyer construction to higher dimensions.
Findings
Constructed models of exotic 8, 10, and Kervaire spheres
Extended the Gromoll-Meyer construction to new dimensions
Provided geometric applications of these models
Abstract
Here we generalize the Gromoll-Meyer construction of an exotic 7-sphere by producing geometric models of exotic 8, 10 and Kervaire spheres as quotients of sphere bundles over spheres by free isometric actions. We give a geometric application at the end.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology · Mathematics and Applications