In this report, we shall discuss the calculations of degree of equivariant mappings about Z_p actions and give a generalization of Borsuk-Ulam theorem about Z_p actions. At first, some notations are introduced. For no...In this report, we shall discuss the calculations of degree of equivariant mappings about Z_p actions and give a generalization of Borsuk-Ulam theorem about Z_p actions. At first, some notations are introduced. For nonnegative integers m,n,〈m,n〉 denotes the greatest common divisor of m and n. m|n means that m is a factor of n. We fix a positive integer p, and展开更多
We confirm the Halperin-Carlsson conjecture for free Z_p-torus actions(p is a prime) on 2-dimensional finite CW-complexes and free Z_2-torus actions on closed 3-manifolds.
I. INTRODUCTIONLet S<sup>2n+1</sup> be the （2n+1）- dimensional standard sphere in complex （n+1） space C<sup>n+1</sup>. Let T: S<sup>2+1</sup>→S<sup>2n+1</sup> be th...I. INTRODUCTIONLet S<sup>2n+1</sup> be the （2n+1）- dimensional standard sphere in complex （n+1） space C<sup>n+1</sup>. Let T: S<sup>2+1</sup>→S<sup>2n+1</sup> be the transformation defined by T（z<sub>0</sub>, z<sub>1</sub>, …, z<sub>n</sub>） = （e （2πi）/p Z<sub>0</sub>, e （2πi）/p Z<sub>1</sub>, …, e （2πi）/p z<sub>n</sub>）, where Z<sub>0</sub>, Z<sub>1</sub>, …, Z<sub>n</sub> are complex numbers with. T acts freely on S<sup>2n+1</sup> and generates a cyclic group Z<sub>p</sub> of order p, and the orbit space is a standard Lens space L<sup>n</sup>（p）.展开更多
文摘In this report, we shall discuss the calculations of degree of equivariant mappings about Z_p actions and give a generalization of Borsuk-Ulam theorem about Z_p actions. At first, some notations are introduced. For nonnegative integers m,n,〈m,n〉 denotes the greatest common divisor of m and n. m|n means that m is a factor of n. We fix a positive integer p, and
基金supported by National Natural Science Foundation of China (Grant No. 11371188)the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD)
文摘We confirm the Halperin-Carlsson conjecture for free Z_p-torus actions(p is a prime) on 2-dimensional finite CW-complexes and free Z_2-torus actions on closed 3-manifolds.
文摘I. INTRODUCTIONLet S<sup>2n+1</sup> be the （2n+1）- dimensional standard sphere in complex （n+1） space C<sup>n+1</sup>. Let T: S<sup>2+1</sup>→S<sup>2n+1</sup> be the transformation defined by T（z<sub>0</sub>, z<sub>1</sub>, …, z<sub>n</sub>） = （e （2πi）/p Z<sub>0</sub>, e （2πi）/p Z<sub>1</sub>, …, e （2πi）/p z<sub>n</sub>）, where Z<sub>0</sub>, Z<sub>1</sub>, …, Z<sub>n</sub> are complex numbers with. T acts freely on S<sup>2n+1</sup> and generates a cyclic group Z<sub>p</sub> of order p, and the orbit space is a standard Lens space L<sup>n</sup>（p）.
