Chain duality VI (Ex)

Latest revision as of 12:06, 30 July 2013

Using Chain duality V (Ex), check that the contravariant functors

$$\displaystyle T \colon \Aa^{\ast} (K) \rightarrow \Bb (\Aa^{\ast} (K)),\\ T \colon \Aa_{\ast} (K) \rightarrow \Bb (\Aa_{\ast} (K)),$$

which are defined in [Ranicki1992, §5] are indeed a chain dualities.

[edit] References

• [Ranicki1992] A. A. Ranicki, Algebraic $<wikitex>; Check that the contravariant functors $T \colon \Aa^{\ast} (K) \rightarrow \Bb (\Aa^{\ast} (K))$ and $T \colon \Aa_{\ast} (K) \rightarrow \Bb (\Aa_{\ast} (K))$ defined in the lecture are indeed a chain dualities using the previous exercise. </wikitex> == References == {{#RefList:}} [[Category:Exercises]] [[Category:Exercises without solution]]L$-theory and topological manifolds, Cambridge University Press, 1992. MR1211640 (94i:57051) Zbl 0767.57002