In the book, Lemma 6.2 (stated below) talks about a corollary of the Thom's isomorphism theorem and Tubular neighbourhood theorem. The proof of the lemma is not provided by the author. And the references for Thom's isomorphism theorem, seems to be incorrect.
Lemma 6.2 Let M and M' are closed connected submanifold of complementary dimensions (r and s respectively) in $V$. Then there is a natural isomorphism $\phi : H_{0}(M') \to H_r(V, V-M')$.
Can anyone provide me a correct reference for this corollary of Thom's isomorphism theorem?
Moreover, I know vector bundle version of Thom's isomorphism theorem. And I am not sure how to deduce Lemma 6.2 from it.
You have written the lemma wrong, it should state there is an isomorphism $H_0 (M') \rightarrow H_r (V,V-M')$. Write $N(M')$ for the normal bundle of $M'$. Since $H_r(V,V-M') \cong H_r(N(M'),N(M')-M')$, the Thom isomorphism is exactly the isomorphism we want to use because the codimension of $M'$ is $r$.