The following is a question from Hatcher's "Algebraic Topology":
Let $M$ is a compact $R$-orientable n manifold, then the boundary map $\partial : H_n(M,\partial M;R) \to H_{n-1} (\partial M)$
sends a fundamental class for $(M,\partial M)$ to a fundamental class for $\partial M$.
Hatcher, however, doesn't treat the fundamental class for a relative homology. I don't know what the fundamental class for $\\(M,\partial M)$ means. Actually, I even have no idea how to define an orientation for a relative homology. Therefore I can't start over. Could you help me?
Best Answer
(Hatcher, Section 3.3, Subsection «Other Forms of Duality»)