共查询到20条相似文献,搜索用时 31 毫秒
1.
J. C. Gómez-Larrañaga F. González-Acuña Wolfgang Heil 《Mathematische Zeitschrift》2008,259(2):419-432
A closed topological n-manifold M
n
is of S
1-category 2 if it can be covered by two open subsets W
1,W
2 such that the inclusions W
i
→ M
n
factor homotopically through maps W
i
→ S
1 → M
n
. We show that the fundamental group of such an n-manifold is a cyclic group or a free product of two cyclic groups with nontrivial amalgamation. In particular, if n = 3, the fundamental group is cyclic.
相似文献
2.
We present a short and direct proof (based on the Pontryagin-Thom construction) of the following Pontryagin-Steenrod-Wu theorem:
(a) LetM be a connected orientable closed smooth (n + 1)-manifold,n≥3. Define the degree map deg: π
n
(M) →H
n
(M; ℤ) by the formula degf =f*[S
n
], where [S
n
] εH
n
(M; ℤ) is the fundamental class. The degree map is bijective, if there existsβ εH
2(M, ℤ/2ℤ) such thatβ ·w
2(M) ε 0. If suchβ does not exist, then deg is a 2-1 map; and (b) LetM be an orientable closed smooth (n+2)-manifold,n≥3. An elementα lies in the image of the degree map if and only ifρ
2
α ·w
2(M)=0, whereρ
2: ℤ → ℤ/2ℤ is reduction modulo 2. 相似文献
3.
Consider the cyclic group C
2 of order two acting by complex-conjugation on the unit circle S
1. The main result is that a finitely dominated manifold W of dimension > 4 admits a cocompact, free, discontinuous action by the infinite dihedral group D
∞ if and only if W is the infinite cyclic cover of a free C
2-manifold M such that M admits a C
2-equivariant manifold approximate fibration to S
1. The novelty in this setting is the existence of codimension-one, invariant submanifolds of M and W. Along the way, we develop an equivariant sucking principle for orthogonal actions of finite groups on Euclidean space. 相似文献
4.
J. C. Gómez-Larra?aga F. González-Acu?a Wolfgang Heil 《Mathematische Zeitschrift》2012,271(1-2):167-173
A closed topological n-manifold M n is of S 1-category 2 if it can be covered by two open subsets W 1, W 2 such that the inclusions W i → M n factor homotopically through maps W i → S 1. We show that for n?>?3, if ${{\rm cat}_{S^1}(M^n )=2}$ then M n is homeomorphic to S n or S n–1 × S 1 or the non-orientable S n–1-bundle over S 1. We also obtain an unknotting theorem for locally flat knots of S n–2 in S n and a characterization of S 1?× S n–1. 相似文献
5.
Zhen Guo 《数学学报(英文版)》2009,25(1):77-84
Let x : Mn^n→ R^n+1 be an n(≥2)-dimensional hypersurface immersed in Euclidean space Rn+1. Let σi(0≤ i≤ n) be the ith mean curvature and Qn = ∑i=0^n(-1)^i+1 (n^i)σ1^n-iσi. Recently, the author showed that Wn(x) = ∫M QndM is a conformal invariant under conformal group of R^n+1 and called it the nth Willmore functional of x. An extremal hypersurface of conformal invariant functional Wn is called an nth order Willmore hypersurface. The purpose of this paper is to construct concrete examples of the 3rd order Willmore hypersurfaces in Ra which have good geometric behaviors. The ordinary differential equation characterizing the revolutionary 3rd Willmore hypersurfaces is established and some interesting explicit examples are found in this paper. 相似文献
6.
WangShiying ZhangYuren LiuYan 《高校应用数学学报(英文版)》1999,14(4):492-494
Abstract. Let Sn be the symmetric group 相似文献
7.
We find the exact asymptotics (asn→∞) of the bestL
1-approximations of classesW
1
r
of periodic functions by spliness∈S
2n, r∼-1
(S
2n, r∼-1
is a set of 2π-periodic polynomial splines of orderr−1, defect one, and with nodes at the pointskπ/n,k∈ℤ) such that V
0
2π
s(
r-1)≤1+ɛ
n
, where {ɛ
n
}
n=1
∞
is a decreasing sequence of positive numbers such that ɛ
n
n
2→∞ and ɛ
n
→0 asn→∞.
Dnepropetrovsk University, Dnepropetrovsk. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 4, pp. 435–444,
April, 1999. 相似文献
8.
Abstract
Thom–Pontrjagin constructions are used to give a
computable necessary and sufficient condition for a homomorphism ϕ
: H
n
(L;Z) → H
n
(M;Z) to be realized by a map
f : M → L of degree k for closed (n − 1)-connected 2n-manifolds M and L,
n > 1. A corollary is that
each (n − 1)-connected
2n-manifold admits selfmaps
of degree larger than 1, n
> 1.
In the most interesting case of dimension 4, with the
additional surgery arguments we give a necessary and sufficient
condition for the existence of a degree k map from a closed orientable
4-manifold M to a closed
simply connected 4-manifold L
in terms of their intersection forms; in particular, there is a
map f :
M → L of degree 1 if and only if the
intersection form of L is
isomorphic to a direct summand of that of
M.
Both authors are supported by MSTC, NSFC. The
comments of F. Ding, J. Z. Pan, Y. Su and the referee enhance
the quality of the paper 相似文献
9.
In a uniform random recursive k-directed acyclic graph, there is a root, 0, and each node in turn, from 1 to n, chooses k uniform random parents from among the nodes of smaller index. If S
n
is the shortest path distance from node n to the root, then we determine the constant σ such that S
n
/log n→σ in probability as n→∞. We also show that max 1≤i≤n
S
i
/log n→σ in probability. 相似文献
10.
11.
Li Banghe 《Commentarii Mathematici Helvetici》1982,57(1):135-144
Under the assumption of (f, M
n
,N
2n−1) being trivial, the classification of immersions homotopic tof: M
n
→N
2n−1 is obtained in many cases. The triviality of (f, M
n
,P
2n−1) is proved for anyM
n
andf.
LetM, N be differentiable manifolds of dimensionn and2n−1 respectively. For a mapf: M → N, denote byI[M, N]
f
the set of regular homotopy classes of immersions homotopic tof. It has been proved in [1] that, whenn>1,I[M, N]
f
is nonempty for anyf. In this paper we will determine the setI[M, N]
f
in some cases.
For example, ifN=P
2n−1 or more generally, the lens spacesS
m
2n−1
=Z
m
/S
2n−1,M is any orientablen-manifold or nonorientable butn≡0, 1, 3 mod 4, then, for anyf, theI[M, N]
f is determined completely.
WhenN=R
2n−1, the setI[M, N] of regular homotopy classes of all immersions has been enumerated by James and Thomas in [2] and McClendon in [3] forn>3. Applying our results toN=R
2n−1 we obtain their results again, except for the casen≡2 mod 4 andM nonorientable.
Whenn=3, McClendon's results cannot be used. Our results include the casesn=3,M orientable or not (for orientableM, I[M, R5] is known by Wu [4]). 相似文献
12.
Yu. A. Kilizhekov 《Mathematical Notes》1996,60(4):378-382
LetW
n
2
M be the class of functionsf: Δ
n
→ ℝ (when Δ
n
is ann-simplex) with bounded second derivative (whose absolute value does not exceedM>0) along any direction at an arbitrary point of the simplex Δ
n
. LetP
1,n
(f;x) be the linear polynomial interpolatingf at the vertices of the simplex. We prove that there exists a functiong ∈ W
n
2
M such that for anyf ∈W
n
2
M and anyx ∈ Δ
n
one has |f
(x)−P
1,
n
(f;x)|≤g(x).
Translated fromMatematicheskie Zametki, Vol. 60, No. 4, pp. 504–510, October, 1996.
I thank Yu. N. Subbotin for posing the problem and for his attention to my work. 相似文献
13.
Carlos Rito 《Geometriae Dedicata》2012,157(1):319-330
We study surfaces of general type S with p
g
= 0 and K
2 = 3 having an involution i such that the bicanonical map of S is not composed with i. It is shown that, if S/i is not rational, then S/i is birational to an Enriques surface or it has Kodaira dimension 1 and the possibilities for the ramification divisor of
the covering map S → S/i are described. We also show that these two cases do occur, providing an example. In this example S has a hyperelliptic fibration of genus 3 and the bicanonical map of S is of degree 2 onto a rational surface. 相似文献
14.
Oscar Perdomo 《Israel Journal of Mathematics》2006,156(1):65-71
Let (S
i, gi),i=1, 2 be two compact riemannian surfaces isometrically embedded in euclidean spaces. In this paper we show that ifM=S
1×S2,then for any functionF: M→R, the graph ofF, i.e. the manifold {(x, F(x)): x∈M}, does not have positive sectional curvature. 相似文献
15.
We extend the scalar curvature pinching theorems due to Peng-Terng, Wei-Xu and Suh-Yang. Let M be an n-dimensional compact minimal hypersurface in S n+1 satisfying Sf 4 f_3~2 ≤ 1/n S~3 , where S is the squared norm of the second fundamental form of M, and f_k =sum λ_i~k from i and λ_i (1 ≤ i ≤ n) are the principal curvatures of M. We prove that there exists a positive constant δ(n)(≥ n/2) depending only on n such that if n ≤ S ≤ n + δ(n), then S ≡ n, i.e., M is one of the Clifford torus S~k ((k/n)~1/2 ) ×S~... 相似文献
16.
Let X
1, X
2, … be a sequence of independent identically distributed real-valued random variables, S
n
be the nth partial sum process S
n
(t) ≔ X
1 + ⋯ X
⌊tn⌋, t ∈ [0, 1], W be the standard Wiener process on [0, 1], and 2 < p < ∞. It is proved that n
−1/2
S
n
converges in law to σW as n → ∞ in p-variation norm if and only if EX
1 = 0 and σ
2 = EX
12 < ∞. The result is applied to test the stability of a regression model.
The research was partially supported by the Lithuanian State Science and Studies Foundation, grant No. T-21/07 相似文献
17.
Roland K. W. Roeder 《Journal of Geometric Analysis》2007,17(1):107-146
Little is known about the global structure of the basins of attraction of Newton’s method in two or more complex variables.
We make the first steps by focusing on the specific Newton mapping to solve for the common roots of P(x, y) = x(1−x) and Q(x,
y) = y2 + Bxy − y.
There are invariant circles S0 and S1 within the lines x = 0 and x = 1 which are superattracting in the x-direction and hyperbolically repelling within the vertical
line. We show that S0 and S1 have local super-stable manifolds, which when pulled back under iterates of N form global super-stable spaces W0 and W1. By blowing-up the points of indeterminacy p and q of N and all of their inverse images under N we prove that W0 and W1 are real-analytic varieties.
We define linking between closed 1-cycles in Wi (i = 0, 1) and an appropriate closed 2 current providing a homomorphism lk: H1 (Wi, ℤ) → ℚ. If Wi intersects the critical value locus of N, this homomorphism has dense image, proving that H1 (Wi, ℤ) is infinitely generated. Using the Mayer-Vietoris exact sequence and an algebraic trick, we show that the same is true
for the closures of the basins of the roots
相似文献
18.
Jianguo Cao 《Frontiers of Mathematics in China》2008,3(4):475-494
In this paper, we study certain compact 4-manifolds with non-negative sectional curvature K. If s is the scalar curvature and W. is the self-dual part of Weyl tensor, then it will be shown that there is no metric g on S
• × S
• with both (i) K > 0 and (ii) ÷ s − W
• ⩾ 0. We also investigate other aspects of 4-manifolds with non-negative sectional curvature. One of our results implies a
theorem of Hamilton: “If a simply-connected, closed 4-manifold M• admits a metric g of non-negative curvature operator, then M• is one of S•, ℂP• and S•×S•”. Our method is different from Hamilton’s and is much simpler. A new version of the second variational formula for minimal
surfaces in 4-manifolds is proved.
相似文献
19.
负相依随机变量的自正则化中心极限定理与部分和的方差估计 总被引:1,自引:0,他引:1
§ 1 IntroductionWe firstintroduce some concepts.Random variables X and Y are called negative dependent ( ND) if for any pair ofmonotonically non-decresing functions f and g,Cov{ f( X) ,g( Y) }≤ 0 .Clearly itis equivalenttoP( X≤ x,Y≤ y)≤ P( X≤ x) P( Y≤ y)for all x,y∈R.A random sequence{ Xi,i≥ 1 } is said to be negative quadrant dependent( NQD) if any pairof variables Xi,Xj( i≠j) are ND.A sequence of random variables{ Xi,i≥ 1 } is said to be linear negative quadrand depend… 相似文献
20.
A hypersurface x : M → S n+1 without umbilic point is called a Möbius isoparametric hypersurface if its Möbius form Φ = ?ρ ?2∑ i (e i (H) + ∑ j (h ij ?Hδ ij )e j (log ρ))θ i vanishes and its Möbius shape operator $ {\Bbb {S}}A hypersurface x : M → S
n
+1 without umbilic point is called a M?bius isoparametric hypersurface if its M?bius form Φ = −ρ−2∑
i
(e
i
(H) + ∑
j
(h
ij
−Hδ
ij
)e
j
(log ρ))θ
i
vanishes and its M?bius shape operator ? = ρ−1(S−Hid) has constant eigenvalues. Here {e
i
} is a local orthonormal basis for I = dx·dx with dual basis {θ
i
}, II = ∑
ij
h
ij
θ
i
⊗θ
i
is the second fundamental form, and S is the shape operator of x. It is clear that any conformal image of a (Euclidean) isoparametric hypersurface in S
n
+1 is a M?bius isoparametric hypersurface, but the converse is not true. In this paper we classify all M?bius isoparametric
hypersurfaces in S
n
+1 with two distinct principal curvatures up to M?bius transformations. By using a theorem of Thorbergsson [1] we also show
that the number of distinct principal curvatures of a compact M?bius isoparametric hypersurface embedded in S
n
+1 can take only the values 2, 3, 4, 6.
Received September 7, 2001, Accepted January 30, 2002 相似文献