论文标题
在非线性graßmannians上引起差异字符
Induced differential characters on nonlinear Graßmannians
论文作者
论文摘要
使用graßmannians上的重言式捆绑包的非线性版本，我们构建了一个从$ m $到非线性graßmannians$ \ mathrm {gr}^s（m）$ m $ $ m $的固定类型$ s $ $ m $ submanifolds的差异图。特别是，我们获得了具有Marsden-Weinstein符号形式的非线性graßmannian的前圆圈束。相关的Kostant-souriau前量扩展产生了整合Lichnerowicz Cocycles的一组量化量的差异的中央谎言组扩展。
Using a nonlinear version of the tautological bundle over Graßmannians, we construct a transgression map for differential characters from $M$ to the nonlinear Graßmannians $\mathrm{Gr}^S(M)$ of submanifolds of $M$ of a fixed type $S$. In particular, we obtain prequantum circle bundles of the nonlinear Graßmannian endowed with the Marsden-Weinstein symplectic form. The associated Kostant-Souriau prequantum extension yields central Lie group extensions of a group of volume-preserving diffeomorphisms integrating Lichnerowicz cocycles.
