摘要
The complex surface X obtained by 8 points blown up on CP2 and Barlow’s surface Y are homeomorphic,but not diffeomorphic.Using the Gromov-Witten invariant Ruan showed that the stabilized manifolds X×S2and Y×S2are not deformation equivalent.In this note,we show that the stabilized manifolds X×S1and Y×S1are diffeomorphic and non-deformation equivalent in cosymplectic sense.
The complex surface X obtained by 8 points blown up on CP2 and Barlow’s surface Y are homeomorphic,but not diffeomorphic.Using the Gromov-Witten invariant Ruan showed that the stabilized manifolds X×S^2and Y×S^2are not deformation equivalent.In this note,we show that the stabilized manifolds X×S^1and Y×S^1are diffeomorphic and non-deformation equivalent in cosymplectic sense.
基金
supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education(Grant No.2013004848)
关键词
稳定流形
微分同胚
复杂曲面
不变量
变形
cosymplectic manifold
symplectic manifold
Gromov-Witten invariant
h-cobordism
Whitehead group
deformation
