论文标题
循环空间的几何形状III：接触歧管的等轴测组
The Geometry of Loop Spaces III: Isometry Groups of Contact Manifolds
论文作者
论文摘要
我们研究了流形的等轴测组$ \ overline {m} _p $，$ p \ in \ mathbb {z} $，它们是封闭的contact contact $（4n+1）$ - 带有封闭reeb轨道的歧管。同等地，$ \ overline {m} _p $是一个封闭的$ 4N $维置符号符号歧管上的圆捆。我们在回路空间上使用wodzicki-chern-simons表单$ l \ overline {m} _p $来证明$π_1（{\ rm isom}（\ rm isom}（\ overline {m} _p））$是$ | p | \ gg 0. $我们还给出了第一个高维wodzicki-pontryagin形式的高维示例。
We study the isometry groups of manifolds $\overline {M}_p$, $p\in\mathbb{Z}$, which are closed contact $(4n+1)$-manifolds with closed Reeb orbits. Equivalently, $\overline{M}_p$ is a circle bundle over a closed $4n$-dimensional integral symplectic manifold. We use Wodzicki-Chern-Simons forms on the loop space $L\overline{M}_p$ to prove that $π_1({\rm Isom}(\overline{M}_p))$ is infinite for $|p| \gg 0.$ We also give the first high dimensional examples of nonvanishing Wodzicki-Pontryagin forms.
