TITLE
On the finiteness and shape of the Universe
AUTHOR
Warren D. Smith
DATE Aug 2004
ABSTRACT
Previous plausible theoretical assumptions about the cosmic 3-manifold, such as
isotropy, orientability, and compactness, have been unable to reduce the number
of candidate topologies to a finite set. We now consider several new possible
assumptions inspired by relationships between microscopic physics and cosmic
topology. The most important are
1. ``No-twist'' assumption that there does not exist a twisted closed geodesic
(to allow photons to exist in momentum-polarization eigenstates),
2. At most one isotopy class of nonseparating surface exists (related
to charge quantization and seems necessary to allow charge to exist),
3. Orthogonal and/or commuting smooth vector fields exist, either locally or globally
(may be needed to generalize quantum mechanics to curved spaces).
We also introduce ``1-curvature homogeneity,'' a weakened version
of the common ``constant curvature'' assumption.
We show that various combinations of these assumptions \emph{are} powerful enough
to winnow the candidate topologies down to a finite set.
We also present new ``reasons for the 3-dimensionality
of the universe'' and a new argument the universe is spatially finite.
KEYWORDS
topology of universe