· | Identify the "orientation" double cover for a general non-orientable surface. |
· |
Suppose p:E --> M is a covering space, with E and M connected n-manifolds. If M is orientable, show that E is orientable, and that every covering transformation preserves orientation. |
· | Problems #2, 5 - 9, Hatcher page 257. |
· | Problems #16, 17, 24, 25, Hatcher page 259. |
· | Prove that a homotopy equivalence CP^{2n} --> CP^{2n} preserves orientation. |
· | Distinguish CP^{2} and S^{2}(wedge) S^{4} preserves orientation. |
· | Distinguish CP^{3} and S^{2}x S^{4} preserves orientation. |
Dan Cohen Fall 2009