April 8th, 2018, 10:04 PM  #1 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 371 Thanks: 26 Math Focus: Number theory  Genus given from pole minima
Can the minimum number of singularities on a three dimensional surface within continuous lines (exhaustively mapped over a topological space) help describe the value of its genus? For instance, think of a globe with two separate poles (singularities) which can be located anywhere on the sphere. The malleable continuous lines may be stretched to accommodate the two poles, but no fewer. This is an example of genuseven. No poles might be needed for genusodd shapes as their holes may interchange topologically like their genusone poles. Each pair of poles (even) corresponds to and transforms into a hole (odd). When forms of differing genera meld, do they conserve the topological properties of poles and holes? So, do genera = f(poles)? 

Tags 
genus, minima, pole 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
pole at infinity  ilikemath123  Complex Analysis  2  February 10th, 2015 07:55 PM 
Finding a pole + integrating  mode1111  Complex Analysis  10  February 8th, 2013 02:31 AM 
Trigonometry: Height of Pole  bilano99  Trigonometry  9  August 2nd, 2012 06:04 PM 
[Help] Genus: Having difficulty to fully understand it.  probiner  Algebra  4  February 17th, 2012 11:49 AM 
retraction on a surface of genus g  d'Artagnan  Real Analysis  0  July 1st, 2011 04:46 PM 