1. A sphere S^n, where n is of the form n = 2*k - 1, is the total
space of a fibre bundle whose fibre is the circle S^1 (and with base
space a complex projective space).
2. A sphere S^n, where n is of the form n = 4*k - 1, is the total
space of a fibre bundle whose fibre is the sphere S^3 (and with base
space a quaternionic projective space).
3. S^15 is the total space of a bundle whose fibre is S^7
(and whose base space is S^8).
4. If n is of the form n = 8*k - 1, then S^n admits a continuous
field of tangent 7-planes.
(See N. Steenrod, Topology of Fibre Bundles, sections 20 and 27.)
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Question:
Do spheres S^n, where n is of the form n = 8*k - 1, for k > 2,
fibre with fibre = S^7 (over some manifold as base space) ?
E.g., is S^23 the total space of a fibre bundle whose fibre
is S^7 ?
Dan Asimov
Mail Stop T045-1
NASA Ames Research Center
Moffett Field, CA 94035-1000
--
Geoffrey Mess
Department of Mathematics, UCLA
Los Angeles, CA.
ge...@math.ucla.edu
NeXTmail welcome.