Germs of fibrations of spheres by great circles always extend to the whole sphere

Cahn, Patricia; Gluck, Herman; Nuchi, Haggai

doi:10.2140/agt.2018.18.1323

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Germs of fibrations of spheres by great circles always extend to the whole sphere

Patricia Cahn, Herman Gluck and Haggai Nuchi

Algebraic & Geometric Topology 18 (2018) 1323–1360

DOI: 10.2140/agt.2018.18.1323

Abstract

We prove that every germ of a smooth fibration of an odd-dimensional round sphere by great circles extends to such a fibration of the entire sphere, a result previously known only in dimension three.

Keywords

fibration, great circles, fiber bundles, Blaschke manifold, spheres

Mathematical Subject Classification 2010

Primary: 53A07, 53C22, 55R10

References

Publication

Received: 20 May 2016

Revised: 27 January 2017

Accepted: 22 February 2017

Published: 3 April 2018

Authors

Patricia Cahn
Department of Mathematics and Statistics Smith College Northampton, MA United States

Herman Gluck
Department of Mathematics University of Pennsylvania Philadelphia, PA United States

Haggai Nuchi
Department of Mathematics University of Toronto Toronto, ON Canada

Volume 18, issue 3 (2018)