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