标题： 带有正标量曲率的大型流形上的圆丛 显示英文标题

标题： Circle bundles with PSC over large manifolds

摘要： 我们构造了无限多个维度为$m \geq 4$的宏观大流形的例子，这些流形配备了其全空间具有正标量曲率度量且宏观维数至多为$\lceil m/2 \rceil + 1$的圆丛。特别地，我们在所有维度上回答了Gromov关于在可扩展流形上的圆丛的全空间是否存在正标量曲率度量的问题。我们的构造基于辛几何的技术。 显示英文摘要

摘要： We construct infinitely many examples of macroscopically large manifolds of dimension $m \geq 4$ equipped with circle bundles whose total spaces admit metrics of positive scalar curvature and have macroscopic dimension at most $\lceil m/2 \rceil + 1$. In particular, we answer a question of Gromov on the existence of circle bundles over enlargeable manifolds whose total spaces admit metrics of positive scalar curvature, in all dimensions. Our constructions are based on techniques from symplectic geometry.