 ### more outline

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 ... ... @@ -160,15 +160,34 @@ We therefore have It was proven by \textcite{hirzebruch_Lgenus}, that this genus coincides with the signature. \end{example} Most of the genus, that are of particular interest, belong to the following class: \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} \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{align*} \end{definition} \begin{remark} \todo[inline]{add motivation} \end{remark} \begin{example} The $\hat{A}$-genus is elliptic.\todo[inline]{extend} The $\hat{A}$-genus can be generalised to the spin bordism ring, where a morphism $\alpha \colon \Omega^{\Spin}_* \to \KO^{-*}(\pt)$ emerges. This map can be represented by a map of spectra $\M \Spin \to \KO$. \end{example} % section introduction_by_julian (end) \section{Ellipctic Genera -- Markus} % (fold) ... ... @@ -180,4 +199,10 @@ We therefore have \label{sec:modular_forms_jens} % section modular_form_jens (end) \section{Formal Group Laws -- Leon} % (fold) \label{sec:formal_group_laws_leon} \todo{looked at chapter 3 in the book} \todo[inline]{maybe not as important for my talk!?} % section formal_group_laws_leon (end) % chapter elliptic_genera_phd_seminar (end) \ No newline at end of file
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