Cheers,

HK

http://arxiv.org/abs/1110.3054 ]]>

Can I ask a question about global topology?

We describe an FRW universe with positive spatial curvature as “closed”, as it has the metric of a three-sphere, but I want to know what this actually means. We derive the three-sphere metric by changing coordinates from r to χ, where χ = Sin(r). Is χ not limited to the interval [0,π/2), since beyond that we are simply reproducing the same r? In which case, is the universe not really one “hemi-threesphere” and not closed in the same way as a full sphere is?

You state in your book that the “only possible global structure is the complete three-sphere”, but you don’t go into why.

The book, btw, is excellent (I particularly enjoy the time you spent at the beginning going into diff. geometry etc, although I still don’t quite get the link, other than notational, between differential forms and integral measures, such that we can integrate p-forms as if they were ordinary integrals).

]]>Many thanks for bringing the lectures to our attention. ]]>