Symbol | Name | \(H_0\) | \(H_1\) | \(H_2\) |
---|---|---|---|---|
\(S^2\) | Sphere | \(\mathbb{Z}^1\) | \(\{0\}\) | \(\mathbb{Z}^1\) |
\(P^2\) | Projective plane | \(\mathbb{Z}^1\) | \(\mathbb{Z}_2\) | \(\{0\}\) |
\(K^2\) | Klein bottle | \(\mathbb{Z}^1\) | \(\mathbb{Z}^1\oplus\mathbb{Z}_2\) | \(\{0\}\) |
\(g\)-holed torus | \(\mathbb{Z}^1\) | \(\mathbb{Z}^{2g}\) | \(\mathbb{Z}^1\) | |
2-Manifold with \(g\) holes and \(c > 0\) cross-caps |
\(\mathbb{Z}^1\) | \(\mathbb{Z}^{2g+c-1}\oplus\mathbb{Z}_2\) | \(\{0\}\) |