- #1
- 7,003
- 10,421
Hi, If we change coefficients in Homology, we can use the universal coefficient theorem
to find the change in the homology group. Still, is there a way of knowing what happens
to _individual classes_ under this change of coefficients? I am just thinking of cases
where there is a major collapse under the coefficient change, like when we go from
Z--integers to Z/2 in, say, S^1 , the unit circle, so that H_1 goes from Z to Z/2;
I guess all classes are collapsed into 2 classes.
Is there a way of knowing what happens to individual classes under this change
?
to find the change in the homology group. Still, is there a way of knowing what happens
to _individual classes_ under this change of coefficients? I am just thinking of cases
where there is a major collapse under the coefficient change, like when we go from
Z--integers to Z/2 in, say, S^1 , the unit circle, so that H_1 goes from Z to Z/2;
I guess all classes are collapsed into 2 classes.
Is there a way of knowing what happens to individual classes under this change
?