Projection to cohomology

Asked Jun 19 '19 at 16:21

Active Jun 19 '19 at 16:52

Viewed 73 times

I have a differential graded algebra $(A,d)$ and $H^*$ be a graded ring.

Let $Z^*=Ker(d)$ and $\alpha:H^*(A)->Z^*$ be a right inverse for the projection to cohomology.

I have the following questions:

1.What is $Z^*$?

(usually with * in the paper the author denotes complexes, like $H^*$, but here...).

2.What is this projection?

Thanks!

edited Jun 19 '19 at 16:52

asked Jun 19 '19 at 16:21

sasho98

Please use mathjax for the mathematical terms. – Con Jun 19 '19 at 16:48
$Z^=\ker d$ as you wrote. What is wrong with that ? With the zero differential it is a complex. As for the projection $H^=Z^/B^$ (where $B^=\operatorname{Im}d$), so the projection is just the canonical map $Z^\to H^*$. – Roland Jun 19 '19 at 18:27

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