相关论文: On Macroscopic dimension of non-spin 4-manifolds

We give a homological characterization of $n$-manifolds whose universal covering $\Wi M$ has Gromov's macroscopic dimension $\dim_{mc}\Wi M<n$. As the result we distinguish $\dim_{mc}$ from the macroscopic dimension $\dim_{MC}$ defined by…

We show that for a rationally inessential orientable closed $n$-manifold $M$ whose fundamental group $\pi$ is a duality group the macroscopic dimension of its universal cover is strictly less than $n$:$$ \dim_{MC}\Wi M<n.$$ As a corollary…

We prove the inequality $$ \dim_{mc}\Wi M\le n-2$$ for the macroscopic dimension of the universal covers $\Wi M$ of almost spin $n$-manifolds $M$ with positive scalar curvature whose fundamental group $\pi_1(M)$ is a virtual duality group…

We study noncompact, complete, finite volume, Riemannian 4-manifolds $M$ with sectional curvature $-1<K<0$. We prove that $\pi_1 M$ cannot be a 3-manifold group. A classical theorem of Gromov says that $M$ is homeomorphic to the interior of…

An irreducible open 3-manifold $W$ is {\bf R}$^2$-irreducible if every proper plane in $W$ splits off a halfspace. In this paper it is shown that if such a $W$ is the universal cover of a connected, {\bf P}$^2$-irreducible open 3-manifold…

We prove that a compact, connected, and oriented 4-dimensional gradient $m$-quasi-Einstein manifold with $m\in [1, \infty]$ which is additionally a spin manifold must satisfy the Hitchin-Thorpe Inequality. We show further that the…

Let $M$ be a 4-dimensional open manifold with nonnegative Ricci curvature. In this paper, we prove that if the universal cover of $M$ has Euclidean volume growth, then the fundamental group $\pi_1(M)$ is finitely generated. This result…

We show that the homotopy type of a 4-manifold $M$ whose fundamental group is a finitely presentable $PD_3$-group $\pi$ and with $w_1(M)=w_1(\pi)$ is determined by $\pi$, $\pi_2(M)$, $k_1(M)$ and the equivariant intersection pairing…

We prove that every finitely generated group with recursive aspherical presentation embeds into a group with finite aspherical presentation. This and several known facts about groups and manifolds imply that there exists a 4-dimensional…

We study closed, oriented 4-manifolds whose fundamental group is that of a closed, oriented, aspherical 3-manifold. We show that two such 4-manifolds are stably diffeomorphic if and only if they have the same w_2-type and their equivariant…

The $\pi_2$-diffeomorphism finiteness result (\cite{FR1,2}, \cite{PT}) asserts that the diffeomorphic types of compact $n$-manifolds $M$ with vanishing first and second homotopy groups can be bounded above in terms of $n$, and upper bounds…

In this note we construct a closed 4-manifold having torsion-free fundamental group and whose universal covering is of macroscopic dimension 3. This yields a counterexample to Gromov's conjecture about the falling of macroscopic dimension.

We construct smooth manifolds with order two $\pi_1$ and even intersection forms which are irreducible, meaning they do not decompose into non-trivial connected sums. Their intersection forms being even implies that their universal covers…

We give a criterion on a group $\pi$ and a homomorphism $w \colon \pi \to C_2$ under which closed $4$-manifolds with fundamental group $\pi$ and orientation character $w$ are classified up to homotopy equivalence by their quadratic…

We show a rigidity theorem for the Seiberg-Witten invariants mod 2 for families of spin 4-manifolds. A mechanism of this rigidity theorem also gives a family version of 10/8-type inequality. As an application, we prove the existence of…

We introduce a topological invariant, it a type of a graph-manifold, which takes natural values. For a 4-dimensional graph-manifold, whose type does not exceed two, it is proved that its universal cover is bi-Lipschitz equivalent to a…

Let $\pi=\pi_1(M)$ for a compact 3-manifold $M$, and let $\chi_4$, $p$ and $q^*$ be the invariants of Hausmann-Weinberger, Kotschick and Hillman respectively. For certain class of compact 3-manifolds $M$, including all those not containing…

In this paper we consider Riemannian manifolds of dimension at least $3$, with nonnegative Ricci curvature and Euclidean Volume Growth. For every open bounded subset with smooth boundary we establish the validity of an optimal Minkowski…

We show that minimal symplectic 4--manifolds with $b_2^+ >1$ and with residually finite fundamental groups are irreducible. We also give examples of irreducible orientable four--manifolds with indefinite intersection forms which are not…

We exhibit the first examples of compact orientable hyperbolic manifolds that do not have any spin structure. We show that such manifolds exist in all dimensions $n \geq 4$. The core of the argument is the construction of a compact…