共查询到20条相似文献,搜索用时 312 毫秒
1.
Anand Dessai 《Mathematische Nachrichten》1998,192(1):159-172
In the first part we give necessary and sufficient conditions for the existence of a stable almost complex structure on a 10-manifold M with H1(M;?) = 0 and no 2-torsion in H1(M;?) for i = 2,3. Using the Classification Theorem of Donaldson we give a reformulation of the conditions for a 4-manifold to be almost complex in terms of Betti numbers and the dimension of the ±-eigenspaces of the intersection form. In the second part we give general conditions for an almost complex manifold to admit infinitely many almost complex structures and apply these to symplectic manifolds, to homogeneous spaces and to complete intersections. 相似文献
2.
For every closed orientable hyperbolic Haken 3-manifold and, more generally, for any orientable hyperbolic 3-manifold M which is homeomorphic to the interior of a Haken manifold, the number 0.286 is a Margulis number. If H 1(M;ℚ) ≠ 0, or if M is closed and contains a semi-fiber, then 0.292 is a Margulis number for M. 相似文献
3.
In this paper we prove that if M is a compact, hyperbolizable 3-manifold, which is not a handlebody, then the Hausdorff dimension of the limit set is continuous
in the strong topology on the space of marked hyperbolic 3-manifolds homotopy equivalent to M. We similarly observe that for any compact hyperbolizable 3-manifold M (including a handlebody), the bottom of the spectrum of the Laplacian gives a continuous function in the strong topology
on the space of topologically tame hyperbolic 3-manifolds homotopy equivalent to M.
Submitted: January 1998. 相似文献
4.
Let (M, ω) be a connected, symplectic 4-manifold. A semitoric integrable system on (M, ω) essentially consists of a pair of independent, real-valued, smooth functions J and H on M, for which J generates a Hamiltonian circle action under which H is invariant. In this paper we give a general method to construct, starting from a collection of five ingredients, a symplectic
4-manifold equipped a semitoric integrable system. Then we show that every semitoric integrable system on a symplectic 4-manifold
is obtained in this fashion. In conjunction with the uniqueness theorem proved recently by the authors, this gives a classification
of semitoric integrable systems on 4-manifolds, in terms of five invariants. 相似文献
5.
Let T be a torus of dimension n > 1 and M a compact T-manifold. M is a GKM manifold if the set of zero dimensional orbits in the orbit space M/T is zero dimensional and the set of one dimensional orbits in M/T is one dimensional. For such a manifold these sets of orbits have the structure of a labelled graph and it is known that
a lot of topological information about M is encoded in this graph.
In this paper we prove that every compact homogeneous space M of non-zero Euler characteristic is of GKM type and show that the graph associated with M encodes geometric information about M as well as topological information. For example, from this graph one can detect whether M admits an invariant complex structure or an invariant almost complex structure. 相似文献
6.
E. A. Sbrodova 《Journal of Mathematical Sciences》2007,144(5):4500-4503
By a slope in the boundary ∂M of a 3-manifold, we mean the isotopy class α of a finite set of disjoint simple closed curves in ∂M that are nontrivial and pairwise nonparallel. In this paper, we construct an algorithm to decide whether or not a given orientable
3-manifold M contains an essential planar surface whose boundary has a given slope α.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 4, pp. 197–202, 2005. 相似文献
7.
Eric Sparla 《Graphs and Combinatorics》1999,15(1):109-125
We prove a centrally-symmetric analogue of the generalized Heawood inequality, i.e. we prove a Lower Bound Theorem for combinatorial
2k-manifolds M whose convex hull is a centrally-symmetric simplicial polytope P under the additional assumptions that M is a subcomplex of the boundary complex of P and that M contains the k-skeleton of P. We also deduce a relation for the minimum number of vertices of a combinatorial 2k-manifold satisfying our Lower Bound.
Received June 12, 1996 Revised June 9, 1997 相似文献
8.
Brian H. Bowditch 《Geometric And Functional Analysis》2007,17(4):1001-1042
Let M be a complete hyperbolic 3-manifold admitting a homotopy equivalence to a compact surface ∑, such that the cusps of M are in bijective correspondence with the boundary components of ∑. Suppose we realise a tight geodesic in the curve complex
as a sequence of closed geodesics M. There is an upper bound on the lengths of such curves in terms of the lengths of the terminal curves and the topologicial
type of ∑. We give proofs of these and related bounds. Similar bounds have been proven by Minsky using the sophisticated machinery
of hierarchies. Such bounds feature in the work of Brock, Canary and Minsky towards the ending lamination conjecture, and
can also be used to study the action of the mapping class group on the curve complex.
Received: January 2006, Revision: March 2007, Accepted: July 2007 相似文献
9.
We classify the complete metrics of nonnegative sectional curvature on M
2 × 2, where M
2 is any compact 2-manifold. 相似文献
10.
S. V. Ivanov 《Geometriae Dedicata》2008,131(1):1-26
We study the computational complexity of basic decision problems of 3-dimensional topology, such as to determine whether a
triangulated 3-manifold is irreducible, prime, ∂-irreducible, or homeomorphic to a given 3-manifold M. For example, we prove that the problem to recognize whether a triangulated 3-manifold is homeomorphic to a 3-sphere, or
to a 2-sphere bundle over a circle, or to a real projective 3-space, or to a handlebody of genus g, is decidable in nondeterministic polynomial time (NP) of size of the triangulation. We also show that the problem to determine whether a triangulated orientable 3-manifold is
irreducible (or prime) is in PSPACE and whether it is ∂-irreducible is in coNP. The proofs improve and extend arguments of prior author’s article on the recognition problem for the 3-sphere.
相似文献
11.
D. B. McReynolds 《Geometriae Dedicata》2007,129(1):47-55
In this article we verify an orbifold version of a conjecture of Nimershiem from 1998. Namely, for every flat n-manifold M, we show that the set of similarity classes of flat metrics on M which occur as a cusp cross-section of a hyperbolic (n + 1)-orbifold is dense in the space of similarity classes of flat metrics on M. The set used for density is precisely the set of those classes which arise in arithmetic orbifolds.
相似文献
12.
Marina Ville 《Geometriae Dedicata》2009,140(1):145-162
Branch points of a real 2-surface Σ in a 4-manifold M generalize branch points of complex curves in complex surfaces: for example, they can occur as singularities of minimal surfaces.
We investigate such a branch point p when Σ is topologically embedded. It defines a link L(p), the components of which are closed braids with the same axis up to orientation. If Σ is closed without boundary, the contribution
of p to the degree of the normal bundle of Σ in M can be computed on the link L(p), in terms of the algebraic crossing numbers of its components and of their linking numbers with one another.
相似文献
13.
T. Etgü 《Acta Mathematica Hungarica》2007,114(3):195-199
We investigate the relationship between the geometry of a closed, oriented 3-manifold M and the symplectic structures on S
1 × M. In most cases the existence of a symplectic structure on S
1 × M and Thurstonșs geometrization conjecture imply the existence of a geometric structure on M. This observation together with the existence of geometric structures on most 3-manifolds which fiber over the circle suggests
a different approach to the problem of finding a fibration of a 3-manifold over the circle in case its product with the circle
admits a symplectic structure.
This work was supported in part by a GEBIP grant from the Turkish Academy of Sciences and a CAREER grant from the Scientific
and Technological Research Council of Turkey. 相似文献
14.
15.
Stéphane Sabourau 《Geometriae Dedicata》2007,127(1):7-18
The systolic volume of a closed n-manifold M is defined as the optimal constant σ(M) satisfying the inequality vol(M, g) ≥ σ(M) sys(M, g)
n
between the volume and the systole of every metric g on M. First, we show that the systolic volume of connected sums of closed oriented essential manifolds is unbounded. Then, we
prove that the systolic volume of every sequence of closed hyperbolic (three-dimensional) manifolds is also unbounded. These
results generalize systolic inequalities on surfaces in two different directions.
相似文献
16.
Michael L. Mihalik 《Commentarii Mathematici Helvetici》1996,71(1):362-372
If a finitely presented groupG is negatively curved, automatic or asynchronously automatic thenG has an asynchronously bounded “almost prefix closed” combing. Results in [Br1] and [E] imply that the fundamental group of any closed 3-manifold satisfying Thurston's geometrization conjecture has an
asynchronously bounded, almost prefix closed combing.
MAIN THEOREM. IfM is a compactP
2-irreducible 3-manifold,π
1 (M) has an asynchronously bounded, almost prefix closed combing, andH, a subgroup ofπ
1 (M), is quasiconvex with respect to this combing, then the cover ofM corresponding toH is a missing boundary manifold. 相似文献
17.
We study spaces obtained from a complete finite volume complex hyperbolic n-manifold M by removing a compact totally geodesic complex (n − 1)-submanifold S. The main result is that the fundamental group of M\ S{M{\setminus} S} is relatively hyperbolic, relative to fundamental groups of the ends of M\ S{M{\setminus} S} , and M\ S{M{\setminus} S} admits a complete finite volume A-regular Riemannian metric of negative sectional curvature. It follows that for n > 1 the fundamental group of M\ S{M{\setminus} S} satisfies Mostow-type Rigidity, has solvable word and conjugacy problems, has finite asymptotic dimension and rapid decay
property, satisfies Borel and Baum-Connes conjectures, is co-Hopf and residually hyperbolic, has no nontrivial subgroups with
property (T), and has finite outer automorphism group. Furthermore, if M is compact, then the fundamental group of M\ S{M{\setminus} S} is biautomatic and satisfies Strong Tits Alternative. 相似文献
18.
B. N. Apanasov 《Annals of Global Analysis and Geometry》1990,8(1):3-12
The paper deals with some geometric approaches (from the viewpoint of (n + 1)- dimentional Lobachevsky geometry) to the deformation theory for uniformized conformal (i.e., flat conformal) structures on a hyperbolic n-manifold M with finite volume. Namely, two kinds of deformations are studied: bendings and stampings along totally geodesic submanifolds of M. The construction of the last deformation disproves a conjecture of C. Kourouniotis. 相似文献
19.
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
20.
Ricci curvature and the topology of open manifolds 总被引:6,自引:0,他引:6
In this paper, we prove that an open Riemannian n-manifold with Ricci curvature and for some is diffeomorphic to a Euclidean n-space if the volume growth of geodesic balls around p is not too far from that of the balls in . We also prove that a complete n-manifold M with is diffeomorphic to if , where is the volume of unit ball in .
Received 5 May, 1997 相似文献