[Cos-top] the Poincare dodecahedral space is better balanced than other spaces

[Boud Roukema]

Dear cos-top friends,

It seems that not only is there at least some interaction
between cosmic topology and gravity - the residual gravity
acceleration effect as derived heuristically for the 1-torus
and 3-torus[1], but the effect distinguishes 3
well-proportioned spaces (T^3, S^3/T^*, S^3/O^*) as special in
that the effect cancels to third order in the Taylor
expansion, and even more interesting, the Poincare
dodecahedral space cancels even better than these other three
well-proportioned spaces. The effect in S^3/I^* cancels down
to fifth order in the Taylor expansion![2] In this sense, it's
better balanced than the other spaces. Maybe we could say that
the former three spaces are well-proportioned and
"well-balanced", while the Poincare space is well-proportioned
and "super-well-balanced"?

This dynamical/geometrical/topological result is independent
of the empirical arguments in favour of the Poincare space.

Enjoy! :)
boud

PS: There'll be a cosmic topology session at the
     12-th Marcel Grossmann Meeting in Paris, 12-18 July 2009.
     http://www.icra.it/MG/mg12/en/
     Contact Marek Demianski and register if you're interested.


[1] RBBSJ, 2007, http://arxiv.org/abs/astro-ph/0602159 Astron.Astrophys.463:861
[2] RR 2009, http://arxiv.org/abs/0902.3402, subm A&A