March 24th, 2017, 06:43 AM  #1 
Newbie Joined: Mar 2016 From: Alabama Posts: 18 Thanks: 0  Homotopy hypothesis
What are the considerations bearing on the conjecture that infinitygroupoids are spaces? Do you consider it likely or unlikely? What do most mathematicians think?

March 24th, 2017, 08:45 AM  #2 
Senior Member Joined: Aug 2012 Posts: 1,414 Thanks: 342 
Why don't you outline what that is, what it means, why it's important, what conclusions you've come to, and where you are stuck in your understanding? Your question is above the level of the typical question here, and I'm sure many of us, myself included, would appreciate a refresher or an introduction to the terminology. Last edited by Maschke; March 24th, 2017 at 08:49 AM. 
March 24th, 2017, 10:26 AM  #3 
Senior Member Joined: Aug 2012 Posts: 1,414 Thanks: 342 
PS  John Baez has a "simplfied" explanation here ...http://math.ucr.edu/home/baez/homotopy/homotopy.pdf Unfortunately it's not simple enough for me. You need to know category theory, ncategories (categories of categories of categories ...), algebraic topology, and a lot of other heavy duty math. The level of the material is at the advanced Ph.D. student (working on thesis) or postdoc. OP, can you say why you asked this question? Are you a postdoc? Or is this something you just ran across online? 
March 24th, 2017, 08:55 PM  #4  
Newbie Joined: Mar 2016 From: Alabama Posts: 18 Thanks: 0  Quote:
 
March 24th, 2017, 10:06 PM  #5  
Senior Member Joined: Aug 2012 Posts: 1,414 Thanks: 342  Quote:
I used to read John Baez's This Weeks Finds articles which is where I heard about ncategories. And I've seen a little category theory in the context of abstract algebra. That's about it for me.  

Tags 
homotopy, hypothesis 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Is connectedness an homotopy invariant?  HubertM  Real Analysis  1  January 19th, 2014 02:19 PM 
straight line homotopyexplain solution  rayman  Real Analysis  2  February 26th, 2013 10:44 AM 
HYPOTHESIS  please help  oliver1  Advanced Statistics  4  April 30th, 2012 06:28 AM 
Algebraic Topology  Homotopy construction  Turloughmack  Topology  1  February 1st, 2011 01:03 PM 
Chain Homotopy Perplexity  signaldoc  Real Analysis  1  February 27th, 2009 02:32 PM 