Hi, everyone:(adsbygoogle = window.adsbygoogle || []).push({});

A couple of points, please:

1) I am reviewing last semester's Simplicial Homology. I was able to do a triangulation

of the torus T^{2}=S^{1}xS^{1}, and I was able to do

a triangulation of T^{2}, although the best I could do was use 18 triangles.

(the triangulation checked out: 18 triangles/faces, 8 vertices, 10 edges)

I tried to do a triangulation with 12 triangles/faces , 6 vertices, but the edges did not

add up ; I need 18, but could only come up with 15.

Anyone know of a smaller triangulation of the Torus (i.e., with fewer than 18 triangles).?. Anyone know how to find the Euler number of general surfaces (like

the Mobius band) , without using Homology (e.g., Betti numbers.).? . I am

trapped in the catch-22 : to find the (simplicial )Homology, I need to find

a triangulation. But to check if the triangulation is a valid one, I need t find

the Euler number, which I only know how to find using the homology group.

2) Is there an algorithm to find the Simplicial Homology of a space X , once X has

been triangulated, and we know the chain groups of X.?. It seems to come

down to some basic calculations, and some basic linear algebra (row-reduction).

Thanks For any Suggestions/Ideas.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Triangulation of Torus, Algorithms for Calculating Simplicial Homology

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**