Timeline for Describing the kernel of the exponential map as a homology group
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 31, 2011 at 2:08 | vote | accept | Andreas Holmstrom | ||
| Mar 30, 2011 at 20:33 | comment | added | Faisal | I don't really know much about abelian varieties, but I can offer a comment that might help. If $G = \mathbb{C}^g/\mathbb{Z}^{2g}$ is a complex torus, then its Lie algebra can be identified with $\mathbb{C}^g$ in such a way that the exponential map may be thought of as the quotient map $\mathbb{C}^g \to G$; in particular, the kernel of exp is $\mathbb{Z}^{2g}$. On the other hand, $G$ is homeomorphic to a product of $2g$ copies of the unit circle, so that $H_1(G,\mathbb{Z}) = \mathbb{Z}^{2g}$. | |
| Mar 30, 2011 at 20:28 | answer | added | mephisto | timeline score: 16 | |
| Mar 30, 2011 at 19:55 | answer | added | Simon Rose | timeline score: 0 | |
| Mar 30, 2011 at 19:12 | history | asked | Andreas Holmstrom | CC BY-SA 2.5 |