My Math Forum  

Go Back   My Math Forum > College Math Forum > Topology

Topology Topology Math Forum


Thanks Tree3Thanks
  • 1 Post By Maschke
  • 1 Post By Maschke
  • 1 Post By Maschke
Reply
 
LinkBack Thread Tools Display Modes
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 infinity-groupoids are spaces? Do you consider it likely or unlikely? What do most mathematicians think?
zambod is offline  
 
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.
Thanks from zambod

Last edited by Maschke; March 24th, 2017 at 08:49 AM.
Maschke is offline  
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, n-categories (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?
Thanks from zambod
Maschke is offline  
March 24th, 2017, 08:55 PM   #4
Newbie
 
Joined: Mar 2016
From: Alabama

Posts: 18
Thanks: 0

Quote:
Originally Posted by Maschke View Post
OP, can you say why you asked this question? Are you a postdoc? Or is this something you just ran across online?
I'm in tech, not math proper. I've worked using dependent type theory. I'm trying to understand the mathematical background of homotopy type theory: https://homotopytypetheory.org/
zambod is offline  
March 24th, 2017, 10:06 PM   #5
Senior Member
 
Joined: Aug 2012

Posts: 1,414
Thanks: 342

Quote:
Originally Posted by zambod View Post
I'm in tech, not math proper. I've worked using dependent type theory. I'm trying to understand the mathematical background of homotopy type theory: https://homotopytypetheory.org/
I know who Voevodsky and the bare basics of HoTT but not much more. I know what a homotopy is anyway. I gather this is related somehow to intuitionist type theory, in which they deny the law of the excluded middle but manage to recover most of modern math anyway.

I used to read John Baez's This Weeks Finds articles which is where I heard about n-categories. And I've seen a little category theory in the context of abstract algebra. That's about it for me.
Thanks from zambod
Maschke is offline  
Reply

  My Math Forum > College Math Forum > Topology

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 homotopy-explain 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





Copyright © 2017 My Math Forum. All rights reserved.