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Detectability of Cosmic Topology in Flat Universes
Recent observations seem to indicate that we live in a universe whose spatial
sections are nearly or exactly flat. Motivated by this we study the problem of
observational detection of the topology of universes with flat spatial
sections. We first give a complete description of the diffeomorphic
classification of compact flat 3-manifolds, and derive the expressions for the
injectivity radii, and for the volume of each class of Euclidean 3-manifolds.
There emerges from our calculations the undetectability conditions for each
(topological) class of flat universes. To illustrate the detectability of flat
topologies we construct toy models by using an assumption by Bernshtein and
Shvartsman which permits to establish a relation between topological typical
lengths to the dynamics of flat models.Comment: 17 pages, 1 figure, latex2e. New references added. Inserted
clarifying points. To appear in Phys. Lett. A (2003) in the present for