Compute Euler Characteristic from Z Homology Dimensions

[lavinia]

The Euler Characterisitc can be computed from the dimensions of the Z homology of a space.
Are there any other invariants that can be computed from the dimensions of the Z homology?

 

[Bacle]

How about the Betti Number.?

 

[lavinia]

How about the Betti Number.?

yes - the Euler Characteristic is the alternating sum of the Betti numbers.

 

[zhentil]

I'm not sure one could say the betti numbers are computed using the dimensions of the Z homology

 

[lavinia]

I'm not sure one could say the betti numbers are computed using the dimensions of the Z homology

right - the betti numbers are the dimensions