Compute Euler Characteristic from Z Homology Dimensions

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lavinia
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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?
 

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How about the Betti Number.?
 
Bacle said:
How about the Betti Number.?

yes - the Euler Characteristic is the alternating sum of the Betti numbers.
 
I'm not sure one could say the betti numbers are computed using the dimensions of the Z homology :smile:
 
zhentil said:
I'm not sure one could say the betti numbers are computed using the dimensions of the Z homology :smile:

right - the betti numbers are the dimensions
 

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