Exercises:Saul - Algebraic Topology - 5/Exercise 5.6
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Exercises
Exercise 5.6
Let [ilmath](X,\mathcal{ J })[/ilmath] be a topological space and let [ilmath]A\in\mathcal{P}(X)[/ilmath] be a retract of [ilmath]X[/ilmath] (with the continuous map of the retraction being [ilmath]r:X\rightarrow A[/ilmath]). Lastly take i [ilmath]i:A\rightarrow X[/ilmath] to be the inclusion map, [ilmath]i:a\mapsto a[/ilmath].
Show that: [ilmath]H_*^s(X)\cong H_*^s(A)\oplus H_*^s(X,A)[/ilmath]
Solution
Notes
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