hi Glenn, Andrew,

The first sentence in your RAS meeting announcement,

"General relativity connects the local geometry of spacetime to the energy contents, but the topology of space is unconstrained."

has been (heuristically) shown to be false since 2006:

http://cdsads.u-strasbg.fr/abs/2007A%26A...463..861R = http://arXiv.org/abs/arXiv:astro-ph/0602159

The small-scale dynamics constrains (in principle) the allowable topologies. The argument is very simple - any of us could have realised this long before 2006 and published it. Now the argument is public - see the paper for the original way of presenting it.

Not only does the effect exist, but different topologies have different dynamical effects, and the Poincare space is special:

http://cdsads.u-strasbg.fr/abs/2009A%26A...502...27R = http://arXiv.org/abs/arXiv:0902.3402

Heuristic arguments can be wrong, so an exact argument for topological accelration was established using an exact GR solution last year:

http://cdsads.u-strasbg.fr/abs/2012CQGra..29p5006O = http://arXiv.org/abs/arXiv:1109.1596

So please, let's finally stop claiming that local geometry and the topology of the spatial section are unrelated!

The second sentence of your announcement is correct, but it's incomplete in that it says nothing about the fact that topology change - for a synchronous, comoving spatial slicing - most likely exists in the moderately early Universe, and possibly at quite recent epochs, purely within *classical* general relativistic cosmology models, without any quantum effects needed. This is perfectly consistent with Geroch's second theorem. This argument is published too:

http://cdsads.u-strasbg.fr/abs/2013PhRvD..87d3521R = http://arXiv.org/abs/arXiv:1201.5845

Cheers Boud

On Wed, 16 Oct 2013, Glenn Starkman wrote:

Date: 13 Dec 2013 Time: 10:30am Location: Burlington House, London http://www.ras.org.uk/about-the-ras/burlington-house

We are pleased to announce a Royal Astronomical Society Specialist Discussion meeting on topology.

General relativity connects the local geometry of spacetime to the energy contents, but the topology of space is unconstrained. Moreover, it is expected that any theory linking quantum mechanics and relativity is likely to exhibit topology change at scales that may have become cosmologically relevant.

Cosmological observations have shown that the Universe is very nearly flat, and that the topology is trivial nearly out to the last scattering surface, but we have no direct measurement of its topology on scales larger than that. This discussion meeting will give an overview of current research in mathematical topology, its application to cosmology and particle physics, and a discussion of recent observations from Planck and other missions. Confirmed keynote speakers include Jeff Weeks (independent) and Philip Candelas (Oxford).