Homology of a cube

[alexdkeros]

Dear Ripser developers,

While trying to compute the persistent homology of a cube, expecting results similar to a 2-sphere, I get the following results:

point cloud
--------------
0.25 0.25 0.25
0.75 0.25 0.25
0.25 0.75 0.25
0.75 0.75 0.25
0.25 0.25 0.75
0.75 0.25 0.75
0.25 0.75 0.75
0.75 0.75 0.75

Results:

The issues are the following:

1.There are only 5 generators of dimension 1.
2.There are no generators in dimension 2.
3.There is a generator in dimension 3 that should ideally be in dimension 2.

Could you please shed some light to this issue?

Thank you in advance,
Alexandros

[ubauer]

Dear Alex,

this result is (surprisingly) correct. It is not too difficult to see that there should only be 5 generators in dimension 1. It is a very interesting and non-obvious exercise to show that there are no generators in dimension 2, but a generator in dimension 3.

Best, Uli