MPEJ Volume 2, No.2, 16pp
Received: August 29, 1995, Revised: March 19, 1996, Accepted: March 20, 1996
Roy R. Douglas
A Canonical Construction Yielding a Global View of Twistor Theory
ABSTRACT: The construction investigated in this paper begins with an ordered,
finite set of closed subgroups of some compact Lie group; from this data, the
construction produces a topological space. Using a combination of fibration
and cofibration techniques, it is possible to describe both the global and the
local topological structure for this space. The construction yields novel,
canonical decompositions of some compact manifolds (including certain spheres),
as well as other interesting spaces with more exotic local topological
structure. With this approach, the correspondences of twistor theory can be
seen in their global geometric context, as a 1-parameter family of such
correspondences, which canonically fit together to form $S^{14}$, a (constant
radius) 14-dimensional sphere in a 15-dimensional Euclidean space.