Let a finite group act semi-freely on a closed symplectic four-manifold with a 2-dimensional fixed point set. Then we show that the relative Gromov-Witten invariants are the same as the invariants on the quotient set-...Let a finite group act semi-freely on a closed symplectic four-manifold with a 2-dimensional fixed point set. Then we show that the relative Gromov-Witten invariants are the same as the invariants on the quotient set-up with respect to the fixed point set.展开更多
The purpose of this paper is to study relations among equivariant operations on 3-dimensional small covers. The author gets three formulas for these operations. As an application, the Nishimura＇s theorem on the const...The purpose of this paper is to study relations among equivariant operations on 3-dimensional small covers. The author gets three formulas for these operations. As an application, the Nishimura＇s theorem on the construction of oriented 3-dimensional small covers and the Lu-Yu＇s theorem on the construction of all 3-dimensional small covers are improved. Moreover, for a construction of 3-dimensional 2-torus manifolds, it is shown that all operations can be obtained by using the equivariant surgeries.展开更多
The symmetries of surfaces which can be embedded into the symmetries of the 3-dimensional Euclidean space R3 are easier to feel by human＇s intuition. We give the maximum order of finite group actions on （R3 E） amon...The symmetries of surfaces which can be embedded into the symmetries of the 3-dimensional Euclidean space R3 are easier to feel by human＇s intuition. We give the maximum order of finite group actions on （R3 E） among all possible embedded closed/bordered surfaces with given geometric/algebraic genus greater than 1 in R3. We also identify the topological types of the bordered surfaces realizing the maximum order, and findsimple representative embeddings for such surfaces.展开更多
基金Supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science, and Technology (2010-0011145)
文摘Let a finite group act semi-freely on a closed symplectic four-manifold with a 2-dimensional fixed point set. Then we show that the relative Gromov-Witten invariants are the same as the invariants on the quotient set-up with respect to the fixed point set.
基金Project supported by Fudan Universitythe Fujyukai Foundation and Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2009-0063179)
文摘The purpose of this paper is to study relations among equivariant operations on 3-dimensional small covers. The author gets three formulas for these operations. As an application, the Nishimura＇s theorem on the construction of oriented 3-dimensional small covers and the Lu-Yu＇s theorem on the construction of all 3-dimensional small covers are improved. Moreover, for a construction of 3-dimensional 2-torus manifolds, it is shown that all operations can be obtained by using the equivariant surgeries.
基金supported by National Natural Science Foundation of China(Grant Nos.11371034 and 11501239)
文摘The symmetries of surfaces which can be embedded into the symmetries of the 3-dimensional Euclidean space R3 are easier to feel by human＇s intuition. We give the maximum order of finite group actions on （R3 E） among all possible embedded closed/bordered surfaces with given geometric/algebraic genus greater than 1 in R3. We also identify the topological types of the bordered surfaces realizing the maximum order, and findsimple representative embeddings for such surfaces.
