泛辛示性式的超渡式和积分公式

On Transgression Forms of Universal Symplectic Characteristic Forms and Integral Formulas

在吴光磊《示性式的超渡》中,给出了陈氏示性式的超渡式和积分公式。本文应用该文中的主要方法和结果,首先定义了四元数Grassmann空间的泛辛示性式Q_r,再在US_p(n)一主丛π_1:Q_(n+m,n)→G_(n+m,n)~Q的相配丛π_3:Q_(n+m,n)^(r-1)→G_(n+m,n)~Q上导出Q_r的超渡式τ_r=i_3~*·h_2~*τ_(2r)。最后得到泛辛示性类的积分公式。

This paper first definites the universal symplectic characteristic formsQ_r of four-number Grassmann space; then deduces the transgression formsτ_r= i_3~*·h_2~*τ_(2r) of Q_r from the associated bandle π_3: Q_((n+m),n)^(r-1)→G_((n+m),n)~Q of universalsymplectic principal fiber bandle π_1: Q_((n+m),n)→G_((n+m),n)~Q; finally gets the inte-gral formulas of universal symplectic chuvacteristic classes.