Algebraic Topology · Problem 2.2.31

Homology — Allen Hatcher

Mathematics — Topology · mayer-vietoris-sequence

Problem

Use the Mayer--Vietoris sequence to show there are isomorphisms

\widetilde{H}_n(X \vee Y) \approx \widetilde{H}_n(X) \oplus \widetilde{H}_n(Y)

if the basepoints of

X

and

Y

that are identified in

X \vee Y

are deformation retracts of neighborhoods

U \subset X

and

V \subset Y