March 26th, 2018, 11:52 PM  #1 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 346 Thanks: 26 Math Focus: Number theory  Limits to topology?
What effect has replacing the spaces of each genusone manifold with a genuszero solid, and vice versa? Is a singularity  solid or spatial  allowed in topology? Can a topology invert universally from a solid or spatial singularity to approach infinity (while conserving their manifold genus), or vice versa? Consider a torus whose hole is stretched into a singularity – what genus is it? Is there an advantage to treating a manifold’s exterior as one more genus? Say the big bang singularity was genus zero. Wouldn’t that property be conserved throughout the present universe? If not, another universe might have interfered, creating simple left and righthanded particles [knots]? Projecting a 4d manifold of genus n onto a 3d surface may yield fewer holes than the original had. 

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limits, topology 
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