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\newtheorem{prop}{Proposition} \newtheorem{cor}{Corollary} \newtheorem*{utheorem}{Theorem} \newtheorem*{ulemma}{Lemma} \newtheorem*{uprop}{Proposition} \newtheorem*{ucor}{Corollary} \theoremstyle{definition} \newtheorem{defn}{Definition} \newtheorem{example}{Example} \newtheorem*{udefn}{Definition} \newtheorem*{uexample}{Example} \theoremstyle{remark} \newtheorem{remark}{Remark} \newtheorem{note}{Note} \newtheorem*{uremark}{Remark} \newtheorem*{unote}{Note} %------------------------------------------------------------------- \begin{document} %------------------------------------------------------------------- \section*{Geometric and topological structures related to M-branes} \hypertarget{context}{}\subsubsection*{{Context}}\label{context} \hypertarget{physics}{}\paragraph*{{Physics}}\label{physics} [[!include physicscontents]] This entry provides hyperlinked keywords and further pointers to the literature for the articles \begin{itemize}% \item [[Hisham Sati]], \emph{Geometric and topological structures related to M-branes} , part I, Proc. Symp. Pure Math. 81 (2010), 181-236 (\href{http://arXiv.org/abs/1001.5020}{arXiv:1001.5020}), part \emph{II: Twisted $String$ and $String^c$ structures}, J. Australian Math. Soc. 90 (2011), 93-108 (\href{http://arxiv.org/abs/1007.5419}{arXiv:1007.5419}); part \emph{III: Twisted higher structures}, Int. J. Geom. Meth. Mod. Phys. 8 (2011), 1097-1116 (\href{http://arxiv.org/abs/1008.1755}{arXiv:1008.1755}) \end{itemize} on phenomena of [[higher geometry]] and [[generalized cohomology]] encountered in [[string theory]] and specifically when going towards [[M-theory]]. Apart from original work this provides an exhaustive bibliography of the relevant existing literature, which we reproduce hyperlinked \hyperlink{BibliographyI}{below}. \hypertarget{contents}{}\section*{{Contents}}\label{contents} \noindent\hyperlink{abstract}{Abstract}\dotfill \pageref*{abstract} \linebreak \noindent\hyperlink{HigherCohomologicalCharges}{Higher cohomological charges}\dotfill \pageref*{HigherCohomologicalCharges} \linebreak \noindent\hyperlink{BibliographyI}{Bibliography of part I}\dotfill \pageref*{BibliographyI} \linebreak \hypertarget{abstract}{}\subsection*{{Abstract}}\label{abstract} \begin{quote}% We consider the topological and geometric structures associated with cohomological and homological objects in [[string theory|M-theory]]. For the latter, we have M2-branes and M5-branes, the analysis of which requires the underlying [[spacetime]] to admit a [[String structure]] and a [[Fivebrane structure]], respectively. For the former, we study how the fields in M-theory are associated with the above structures, with [[L-infinity algebra|homotopy algebras]], with [[twisted cohomology]], and with [[cohomology|generalized cohomology]]. We also explain how the corresponding charges should take values in [[topological modular form]]s. We survey background material and related results in the process. \end{quote} \hypertarget{HigherCohomologicalCharges}{}\subsection*{{Higher cohomological charges}}\label{HigherCohomologicalCharges} Discussion of [[elliptic cohomology]] and [[Morava K-theory]] as the home for higher analogs of [[D-brane charges]] ([[M5-brane charge]], [[M9-brane]] charge\ldots{}) and the corresponding [[orientation in generalized cohomology]] as higher [[quantum anomaly]] conditions (such as the [[Diaconescu-Moore-Witten anomaly]]): \begin{itemize}% \item [[Hisham Sati]], [[Craig Westerland]], \emph{Twisted Morava K-theory and E-theory} (\href{http://arxiv.org/abs/1109.3867}{arXiv:1109.3867}) \item [[Igor Kriz]], [[Hisham Sati]], \emph{M-theory, type IIA superstrings, and elliptic cohomology}, Adv. Theor. Math. Phys. 8 (2004), no. 2, 345--394 (\href{http://arxiv.org/abs/hep-th/0404013}{arXiv:hep-th/0404013}) \end{itemize} \begin{itemize}% \item [[Lukas Buhné]], \emph{[[Properties of Integral Morava K-Theory and the Asserted Application to the Diaconescu-Moore-Witten Anomaly]]}, Diploma thesis Hamburg (2011) \end{itemize} \hypertarget{BibliographyI}{}\subsection*{{Bibliography of part I}}\label{BibliographyI} \{AKMW\} [[Orlando Alvarez]], T. P. Killingback, M. L. Mangano, and P. Windey, \emph{String theory and loop space index theorems}, Commun. Math. Phys. \textbf{111} (1987) 1-10, \href{http://projecteuclid.org/euclid.cmp/1104159462}{euclid}, \href{http://www.ams.org/mathscinet-getitem?mr=0896755}{MR0896755} \{ASi\} [[Orlando Alvarez]] and I. M. 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