# Talk:Chain duality V (Ex)

From Manifold Atlas

This is immediate from the definition that .

Somewhat more elaborate, so that we really can see what's going on:

given by

This sequence of maps is precisely the previously mentioned . (which has hopefully been treated in the solution to exercise 10 on L-groups) Applying this map to , we get , which is equal to the identity map, as part of its very definition.