相关论文: Quotients of $S^2\times{S^2}$

We construct a new 7-dimensional manifold with positive sectional curvature which is 2-connected with \pi_3=\Z_2 and admits an isometric group action with one dimensional quotient.

We prove that a topological 4-manifold of globally non-positive curvature is homeomorphic to Euclidean space.

We describe of the topology of the geometric quotients of 2n dimensional compact connected symplectic manifolds with n-1 dimensional torus actions. When the isotropy weights at each fixed point are in general position, the quotient is…

We formulate a conjecture that arithmetic locally symmetric manifolds have simple homotopy type, and prove it for the non-compact case. More precisely, we show that, for any symmetric space S of non-compact type without Euclidean de Rham…

We show that for every odd prime $q$, there exists an infinite family $\{M_i\}_{i=1}^{\infty}$ of topological 4-manifolds that are all stably homeomorphic to one another, all the manifolds $M_i$ have isometric rank one equivariant…

In this paper we study $\mathcal M(X)$, the set of diffeomorphism classes of smooth manifolds with the simple homotopy type of $X$, via a map $\Psi$ from $\mathcal M(X)$ into the quotient of $K(X)=[X,BSO]$ by the action of the group of…

We show that the homotopy type of a finite oriented Poincar\'{e} 4-complex is determined by its quadratic 2-type provided its fundamental group is finite and has a dihedral Sylow 2-subgroup. By combining with results of Hambleton-Kreck and…

Any smooth, closed oriented 4-manifold has a surface diagram of arbitrarily high genus g>2 that specifies it up to diffeomorphism. The goal of this paper is to prove the following statement: For any smooth, closed oriented 4-manifold M,…

We compute the topological simple structure set of closed manifolds which occur as total spaces of flat bundles over lens spaces S^l/(Z/p) with fiber an n-dimensjional torus T^n for an odd prime p and l greater or equal to 3, provided that…

Let M be a closed simply connected n-manifold of positive sectional curvature. We determine its homeomorphism or homotopic type if M also admits an isometric elementary p-group action of large rank. Our main results are: There exists a…

We calculate the homology groups of certain 2-connected 7-manifolds admitting quasi-regular Sasaki-Einstein metrics. These manifolds are links that arise as Thom-Sebastiani sums of chain type singularities and cycle type singularities.…

Quoric manifolds are the quaternionic analogue of toric manifolds. They admit a locally nice action of $(S^3)^n$ and the quotient is a manifold with corners. We show that they satisfy equivariant rigidity. More precisely, any locally linear…

A homeomorphism of a compact metric space is {\em tight} provided every non-degenerate compact connected (not necessarily invariant) subset carries positive entropy. It is shown that every $C^{1+\alpha}$ diffeomorphism of a closed surface…

This paper gives the classifications of certain manifolds $\mathcal{M}$ of dimension $13$ up to diffeomorphism, homeomorphism, and homotopy equivalence, whose cohomology rings are isomorphic to $H^\ast(\mathrm{CP}^3\times S^7;\mathbb{Z})$.…

For most aspherical Seifert-fibered 3-manifolds $M$, the space of Seifert fiberings $SF(M)$ is known to have contractible components. It is also known that the space of Hopf fiberings of the three-sphere is noncontractible. We provide the…

There are many theorems in the differential geometry literature of the following sort. Let M be a complete Riemannian manifold with some conditions on various curvatures, diameters, volumes, etc. Then M is homotopy equivalent to a finite CW…

This paper studies the set of finite groups appearing as $\pi_1(M)/\pi_1(M)^{(n)}$, where $M$ is a closed, orientable 3-manifold and $\pi_1(M)^{(n)}$ denotes the $n$-th term of the derived series of $\pi_1(M)$. Our main result is that if…

Let $G$ be a simply-connected simple compact Lie group and let $M$ be an orientable smooth closed 4-manifold. In this paper we calculate the homotopy type of the suspension of $M$ and the homotopy types of the gauge groups of principal…

We study oriented closed manifolds M^n possessing the following Universal Realisation of Cycles (URC) Property: For each topological space X and each integral homology class z of it, there exist a finite-sheeted covering \hM^n of M^n and a…

In this paper we prove a single exponential upper bound on the number of possible homotopy types of the fibres of a Pfaffian map, in terms of the format of its graph. In particular we show that if a semi-algebraic set $S \subset…