In this paper, we prove two theorema on immersions of Dold manifolds P(m, n). Let A_1={(2~s,0): s≥1};A_2={(0,2~s): s≥1}; A_3={(2~s,2~t):0≤s≤t};A_4={(2~s-1, 1): s=1}; A_5={(m,2~t): 2^(t+1)≤m, (2m+2^(t+1)-1)≡1 mod...In this paper, we prove two theorema on immersions of Dold manifolds P(m, n). Let A_1={(2~s,0): s≥1};A_2={(0,2~s): s≥1}; A_3={(2~s,2~t):0≤s≤t};A_4={(2~s-1, 1): s=1}; A_5={(m,2~t): 2^(t+1)≤m, (2m+2^(t+1)-1)≡1 mod2}. We heve Theorem 1 Nonorientable P(m, n) immerses in R^(2m+4n-2) iff (m, n)(?)A_1. Theorem 2 (ⅰ) If (m, n)=(4s+2, 2t), s>0, then P (m, n) immerses in R^(2m+4n-3) iff (m, n)(?)A_3∪A^5. (ⅱ) If (m, u)=(4s, 2t), then P (m, n) immerses in R^(2m+4n-3) iff s>0 anb (m, n) A_1∪A_3∪A_5, or s=0 anb a(t)>2. (ⅲ) If (m, n)=4s+1, 2t), then P(m, n) immerses in R^(2m+4n-3) iff(m, n)A_3∪A_5; if (m, n)=(4s+3, 2t+1), then P(m, n) immerses in R^(2m+4n-3) iff (m, n)A_4. Theorem 2 (ⅲ) corrects an error in the paper [1] of Ucci concerning the case(m, n)=(4s+1, 2t).展开更多
Let J_(*,k)~r 2. denote the ideal in MO_* of cobordism classes containing arepresentative that admits (Z_2)~k-actions with a fixed point set of constant codimension r. Inthis paper we determine J_(*,k)^(2^k+2) and J_(...Let J_(*,k)~r 2. denote the ideal in MO_* of cobordism classes containing arepresentative that admits (Z_2)~k-actions with a fixed point set of constant codimension r. Inthis paper we determine J_(*,k)^(2^k+2) and J_(*,3)^(2^3+1).展开更多
There are two algebraic lower bounds of the number of n-periodic points of a self-map f ： M → M of a compact smooth manifold of dimension at least 3： NFn（f） = min{#Fix（gn）;g - f; g is continuous} and NJDn（f） ...There are two algebraic lower bounds of the number of n-periodic points of a self-map f ： M → M of a compact smooth manifold of dimension at least 3： NFn（f） = min{#Fix（gn）;g - f; g is continuous} and NJDn（f） = min{#Fix（gn）; g - f; g is smooth}. In general, NJDn（f） may be much greater than NFn（f）. If M is a torus, then the invariants are equal. We show that for a self-map of a nonabelian compact Lie group, with free fundamental group, the equality holds 〈=〉 all eigenvalues of a quotient cohomology homomorphism induced by f have moduli ≤ 1.展开更多
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 paper, we prove two theorema on immersions of Dold manifolds P(m, n). Let A_1={(2~s,0): s≥1};A_2={(0,2~s): s≥1}; A_3={(2~s,2~t):0≤s≤t};A_4={(2~s-1, 1): s=1}; A_5={(m,2~t): 2^(t+1)≤m, (2m+2^(t+1)-1)≡1 mod2}. We heve Theorem 1 Nonorientable P(m, n) immerses in R^(2m+4n-2) iff (m, n)(?)A_1. Theorem 2 (ⅰ) If (m, n)=(4s+2, 2t), s>0, then P (m, n) immerses in R^(2m+4n-3) iff (m, n)(?)A_3∪A^5. (ⅱ) If (m, u)=(4s, 2t), then P (m, n) immerses in R^(2m+4n-3) iff s>0 anb (m, n) A_1∪A_3∪A_5, or s=0 anb a(t)>2. (ⅲ) If (m, n)=4s+1, 2t), then P(m, n) immerses in R^(2m+4n-3) iff(m, n)A_3∪A_5; if (m, n)=(4s+3, 2t+1), then P(m, n) immerses in R^(2m+4n-3) iff (m, n)A_4. Theorem 2 (ⅲ) corrects an error in the paper [1] of Ucci concerning the case(m, n)=(4s+1, 2t).
文摘In this paper the following problem has been completely solved:when is a map f:P（m‘n）→CP<sup>?</sup> homotopic to an immersion with codimension one or
基金Supported by the National Natural Sciences Foundation of P.R.China(No.10371029)the Natural Sciences Foundation of Hebei Province(No.103144)the Doctoral Foundation of Hebei Normal University(No.103257)
文摘Let J_(*,k)~r 2. denote the ideal in MO_* of cobordism classes containing arepresentative that admits (Z_2)~k-actions with a fixed point set of constant codimension r. Inthis paper we determine J_(*,k)^(2^k+2) and J_(*,3)^(2^3+1).
文摘There are two algebraic lower bounds of the number of n-periodic points of a self-map f ： M → M of a compact smooth manifold of dimension at least 3： NFn（f） = min{#Fix（gn）;g - f; g is continuous} and NJDn（f） = min{#Fix（gn）; g - f; g is smooth}. In general, NJDn（f） may be much greater than NFn（f）. If M is a torus, then the invariants are equal. We show that for a self-map of a nonabelian compact Lie group, with free fundamental group, the equality holds 〈=〉 all eigenvalues of a quotient cohomology homomorphism induced by f have moduli ≤ 1.
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）.
