Timeline for Homology with Coefficients
Current License: CC BY-SA 2.5
2 events
| when toggle format | what | by | license | comment | |
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| Mar 21, 2010 at 21:00 | comment | added | Tony Huynh | Perhaps I should be more explicit about the function that I am describing. It is a function $h$ from the closed walks (cycles) of the group-labelled graph $G$ into the group $\Gamma$. Explicitly, $h$ maps a cycle $C$ to the (oriented) sum of the group-labels of the edges of $C$. With the condition that all faces of $G$ have group-value zero, this map becomes well-defined on homology. Let $C_1$ and $C_2$ be homologous. Then, $C_1 \cup C_2$ is the boundary of an orientable component of $S - C_1 \cup C_2$. Since each face of $G$ has group-value zero, we have $h(C_1)-h(C_2)=0$, as required. | |
| Mar 20, 2010 at 20:57 | history | answered | Theo Johnson-Freyd | CC BY-SA 2.5 |