覆盖空间中的庞开来对偶

Poincare Duality in Covering Spaces

庞开来对偶定理反应了流形中同调与上同调之间的一种对称性.正则覆盖空间作为流形具有很多良好的性质.研究在正则覆盖空间情况下,得出庞开来对偶的一类特殊性质,即底空间的上同调庞开来对偶通过覆盖映射的拉回仍为庞开来对偶.

Poincare duality reflect a strong symmetry on the homology and cohomology groups of manifolds,and regular covering space as a manifold has a lot of good character.In this paper,a special connection of Poincare duality in regular covering space is acquired.It shows that the pull-back of Poincare pairing via covering map in the base space is still Poincare pairing.