\title{Kletki Shuberta na lagranzhevom grassmaniane} \author{Viktor Kryukov} \date{24 oktyabrya 2000} \begin{abstract} Rassmotrim kompleksnyj \emph{lagranzhev grassmanian}~$\Lambda_n$~--- mnozhestvo lagranzhevykh ploskostej v simplekticheskom prostranstve~$C^{2n}$. S lagranzhevym grassmanianom svyazano \emph{tavtologicheskoe rassloenie}~$L$ --- podmnozhestvo $\Lambda_n\times C^{2n}$, obrazovannoe takimi parami $(F,x)$, chto $x\in F$. Okazyvaetsya, kol'co kogomologij $\Lambda_n$ porozhdaetsya klassami Cherna $c_i(L)$. Drugoj bazis v kol'ce kogomologij $\Lambda_n$ porozhdaetsya klassami, dvojstvennymi k kletkam Shuberta kletochnogo razbieniya lagranzhevogo grassmaniana (ehto razbienie analogichno kletochnomu razbieniyu obychnogo grassmaniana). My privodim formuly, svyazyvayushchie ehti dva bazisa: klassy, dvojstvennye k kletkam Shuberta, vyrazhayutsya cherez klassy Cherna tavtologicheskogo rassloeniya s pomoshch'yu pfaffiana. Poluchayushchiesya formuly mozhno sravnit' s formulami Dzhambeli, kotorye vyrazhayut klassy, dvojstvennye k kletkam Shuberta obychnogo grassmaniana, cherez opredelitel' ot klassov Cherna. \end{abstract}