# Compact connected orientable manifold

Given a compact connected orientable manifold of dimension $n$, the $n^{th}$ homology is isomorphic to $\mathbb{Z}$, and choosing a generator is tantamount to choosing an orientation. A generator for this is termed a fundamental class for the manifold, and maps between compact connected orientable manifolds are often studied in terms of their degree, which is the integer $d$ such that the fundamental class of the manifold on the left goes to $d$ times the fundamental class on the right.