what's the genus of the universe?

[AntonioLao]

formally speaking, genus is a topological invariant property of a surface. Informally, it is the number of holes in a given surface. Clarified at

http://mathworld.wolfram.com/Genus.html

if the universe has 2 holes then its topology is that of a double torus.

[Guille]

Now I know what a genus is, I think that these "holes" of the universe could be black holes....or maybe wormholes....or/and whiteholes.....if it's any of these three, I guess there must be at least more than 100.

[AntonioLao]

The 1st hole of the universe is the Big Bang singularity. I don't know what's the second hole?

[Guille]

Maybe a big bang singularity inside this universe, but which didn't continue to grow: it sort of "died" prematurely, but staid there for ever.

[AntonioLao]

What I meant was what is it that's going in and out of the 2nd hole?

[Guille]

Is there anything that goes in and out of the 1st hole (bb starting point)? Is it necessary(if yes, why?) for the holes to have things going in and out? Aren't the singularities of BH the same as the BB singularity? And the same as the micro-singularities? If yes, why does it have to be 2 holes?

[AntonioLao]

The BB singularity is the hole where everything originally comes out of. The black hole singularities only apply for collapsing stars and galaxies and quasars, etc. where things go back into the holes. But the BH singularities are not true singularities because of the event horizons unless they are naked singularities but as asserted by Penrose's cosmic censorship, naked singularities cannot exist.

[Guille]

Maybe what comes from the second hole is the matter that goes into the black holes and reach the very end, without disintegration (or whatever it's called)?

[AntonioLao]

But if the universe is a one-sided surface, what goes in can only come back to the same universe.

[Guille]

But if the universe is a one-sided surface, what goes in can only come back to the same universe.

Yes, exactly, the hole I'm talking about is in our universe, it's a "failed" bb singularity which remains there, and acts as the returning point for the BH matter.