Commit a528c73f by Jannes Bantje

### add definition of elliptic genus

parent b0dfbd3d
Pipeline #59539 passed with stages
in 27 seconds
 ... @@ -159,6 +159,16 @@ We therefore have ... @@ -159,6 +159,16 @@ We therefore have The genus obtained by this power series is called \Index[L-genus@$L$-genus]{$L$-genus}. The genus obtained by this power series is called \Index[L-genus@$L$-genus]{$L$-genus}. It was proven by \textcite{hirzebruch_Lgenus}, that this genus coincides with the signature. It was proven by \textcite{hirzebruch_Lgenus}, that this genus coincides with the signature. \end{example} \end{example} \begin{definition} A genus $\varphi$ is called an \Index[genus!elliptic]{elliptic genus}, if the corresponding power seires $f(x)=x/Q(x)$ satisfies on of the three equivalent conditions: \begin{align} (f')^2 &= 1- 2 \delta \cdot f^2 + \varepsilon \cdot f^4 \\ f(u+v) &= \frac{f(u)f'(v) + f'(u)f(v)}{1- \varepsilon \cdot f(u)^2 f(v)^2} \\ f(2u) &= \frac{2f(u)f'(u)}{1-\varepsilon \cdot f(u)^4} \end{align} \end{definition} % section introduction_by_julian (end) % section introduction_by_julian (end) \section{Ellipctic Genera -- Markus} % (fold) \section{Ellipctic Genera -- Markus} % (fold) ... ...
Markdown is supported
0% or
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment