Wiki discussion

Discussion of shapes with curves and holes in various dimensions.

Wiki discussion

Postby PWrong » Wed Dec 02, 2009 5:53 am

Let's use this thread for talking about wiki articles on toratopes and homology groups.

I just have a couple of things to say for now.

1. I'm not sure about using vertical bars instead of numbers for toratopic notation. ((II)II) makes the dimension slightly more obvious, but (211) is a lot easier to read and it's still easy to add up the numbers.

2. The word for shapes that have the same homology groups is homeomorphic. I don't think homologous means anything in topology.


Also, I'll collect some of the rules I've come up with here, so we can put them in the wiki somewhere and make a table.

1. Cartesian products of two hyperspheres
HqSa x Sb = h0 + ha + hb + ha+b

This means that if a \= b then
H0 = Z
Ha = Z
Hb = Z
Ha+b =Z
and everything else is zero.

2. Cartesian product of anything with a circle
Hq A2 = Hq A ⊕ Hq-1 A
User avatar
PWrong
Pentonian
 
Posts: 1599
Joined: Fri Jan 30, 2004 8:21 am
Location: Perth, Australia

Re: Wiki discussion

Postby Keiji » Wed Dec 02, 2009 7:03 am

PWrong wrote:1. I'm not sure about using vertical bars instead of numbers for toratopic notation. ((II)II) makes the dimension slightly more obvious, but (211) is a lot easier to read and it's still easy to add up the numbers.


Vertical bars are consistent, as in they can be used everywhere. Numbers can only be used for the innermost groups, if you then replace all the remaining bars with ones. Plus, it converts to a surface equation faster (the method to convert to surface equation requires that you're using the vbars first). You also don't need to know that n === (In), so it's more intuitive.
User avatar
Keiji
Administrator
 
Posts: 1984
Joined: Mon Nov 10, 2003 6:33 pm
Location: Torquay, England

Re: Wiki discussion

Postby PWrong » Wed Dec 02, 2009 7:10 am

Alright. We should make it clear though that using numbers is a common shorthand, especially for smaller shapes.

I've written an article on homology groups. It could use a lot of work though.
http://teamikaria.com/hddb/wiki/Homology_groups
User avatar
PWrong
Pentonian
 
Posts: 1599
Joined: Fri Jan 30, 2004 8:21 am
Location: Perth, Australia

Re: Wiki discussion

Postby Keiji » Wed Dec 02, 2009 7:13 am

Numbers are used for rotatopes (and tapertopes) because they don't use spheration, only base hyperspheres. But yeah, I'll add a note on that.
User avatar
Keiji
Administrator
 
Posts: 1984
Joined: Mon Nov 10, 2003 6:33 pm
Location: Torquay, England

Re: Wiki discussion

Postby PWrong » Wed Dec 02, 2009 7:18 am

I've just done it, on the toratopic notation article.
User avatar
PWrong
Pentonian
 
Posts: 1599
Joined: Fri Jan 30, 2004 8:21 am
Location: Perth, Australia


Return to Toratopes

Who is online

Users browsing this forum: No registered users and 12 guests