S-duality I (Ex)
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Let and be a finite pointed CW-complexes. A map
is called an S-duality if the slant product induced by
is an isomorphism for all . In this case and are called an -duals of each other.
Exercise 0.1. Show that -duality satisfies the following"
- For every finite CW-complex there exists an -dimensional S-dual, which we denote , for some large .
- If is an -dimensional -dual of then is an -dimensional -dual of .
- For any space we have isomorphisms
- A map induces a map for large enough via the isomorphism
- If is a cofibration sequence then is a cofibration sequence for large enough.