March 26th, 2018, 11:52 PM  #1 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 397 Thanks: 27 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. 

Tags 
limits, topology 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
topology  aminea95  Topology  1  January 7th, 2018 02:23 PM 
Problem on product topology/standard topology on R^2.  vercammen  Topology  1  October 19th, 2012 11:06 AM 
Limits,Finding functions by limits  kadmany  Calculus  9  March 18th, 2011 06:16 AM 
discrete topology, product topology  genoatopologist  Topology  0  December 6th, 2008 10:09 AM 
discrete topology, product topology  Erdos32212  Topology  0  December 2nd, 2008 01:04 PM 