Cohomology of the Heisenberg Manifold Sequence

We describe the cohomological structure of the sequence of Heisenberg nilmanifolds MH2n-1→MH2n+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M}_{H}^{2n-1}\to {M}_{H}^{2n+1}$$\end{document}, n = 1, 2, . . . , in terms of bigraded symplectic structures on the tori T2n, the corresponding sl2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{s}\mathfrak{l}}_{2}$$\end{document}-representations on the cohomology of T2n, and the Buchstaber spectral sequence (Bss).