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Euler char, compactifications and supernumerary theoriesPosted by Sauron on January 29, 2003 at 20:09:54: I have been refreshing my knowledges in fibre bundles and i have found an aparent incompatibility. In compactificatios of strings the Euler char. of the manifold gives us the number of families, so it must be diferent from 0. In supernumerary theories gravity travels throught those compactified dimensions, but these means that there must be a globaly defined lorentzian metric in order to have it defned. But the condition for global existance of a Lorentzian metric is that the Euler char. would be 0. So aparently these would mean that supernumerary theories and gauge theories by kaluza mechanism and 3 families would be uncompatible. I suposse that i am missing something, so my question is where is the point which compatibilzates boths.
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