POSTED AR AMAZON 2009
Unique topic that has not been explored in any cosmology book I know..
I fully agree with earlier reviews. It is a beautiful and important book that will expand any cosmology follower's knowledge. I have never encountered a cosmic topology subject in numerous publications dealing with Universe (please see my Listmania). I had no idea of topology role in establishing whether global shape of space is finite or infinite.
Briefly: we learn, that for spherical finite space general relativity shows how to indirectly measure the curvature of the space. Its value depends on the average density of matter/energy that it contains. However for the geometries of the two other families, Euclidean and hyperbolic, the finite or infinite character of space no longer depends simply on the curvature and on the energy density: it depends on the TOPOLOGY !
While for decades observational cosmology pushed itself to determine the curvature parameters directly while neglecting the topological possibilities, it could be that in the XXI century, it would be primarily the experimental determination of the topology of the Universe that would allow us to fix, with great precision, the curvature and the cosmological constant - those traditional parameters on which the ultimate fate of the cosmos depends: perpetual expansion or eventual contraction. Is theory of Big Bang truly valid and confirmed? - author presents its limits and simplifications. However I must admit that some parts of the book are not easy, as reader is asked to jump from two to three dimensions. This require stretching imagination to the limit (chapters about multiply connected spaces leading to cosmic crystallography methods). Lack of glossary of terms is detrimental, particularly, because there are many of them here, not to be found in other cosmology books. Nevertheless it is fascinating lecture - do not miss it !