Related papers: Cancellation for 4-manifolds with virtually abelia…

Main Theorem (3.3): Let $M$ be a compact four-dimensional manifold either with curvature, positive on complex isotropic two-planes, or self-dual of positive scalar curvature. If $\pi_1 (M)$ admits a nontrivial unitary representation, and…

Let M be a closed 5-manifold of pinched curvature 0<\delta\le \text{sec}_M\le 1. We prove that M is homeomorphic to a spherical space form if M satisfies one of the following conditions: (i) \delta =1/4 and the fundamental group is a…

Given any topological group $G$, the topological classification of principal $G$-bundles over a finite CW-complex $X$ is long-known to be given by the set of free homotopy classes of maps from $X$ to the corresponding classifying space…

Let $(X,\omega)$ be a compact symplectic manifold of dimension $2n$ and let $Ham(X,\omega)$ be its group of Hamiltonian diffeomorphisms. We prove the existence of a constant $C$, depending on $X$ but not on $\omega$, such that any finite…

We study the space $Q_n$ of all configurations of $n$ ordered points on the circle such that no three points coincide, and in which one of the points (say, the last one) is fixed. We compute its fundamental group for $n<6$ and describe its…

The objective of this paper is to study the anabelian object referred to as \emph{pointed virtual curves}. Namely, given a family of curves $Y \rightarrow X$ over a field $k$ under suitable conditions, we consider the…

A smooth five-dimensional s-cobordism becomes a smooth product if stabilized by a finite number n of $S^2xS^2x[0,1]$'s. We show that for amenable fundamental groups, the minimal n is subextensive in covers, i.e., n(cover)/index(cover) has…

We give constraints on smooth families of 4-manifolds with boundary using Manolescu's Seiberg-Witten Floer stable homotopy type, provided that the fiberwise restrictions of the families to the boundaries are trivial families of 3-manifolds.…

Let M be an irreducible smooth projective variety defined over \bar{{\mathbb F}_p}. Let \pi(M, x_0) be the fundamental group scheme of M with respect to a base point x_0. Let G be a connected semisimple linear algebraic group over…

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…

A compact topological space X is spectral if it is sober (i.e., every irreducible closed set is the closure of a unique singleton) and the compact open subsets of X form a basis of the topology of X, closed under finite intersections.…

Consider a proper cocompact CAT(0) space X. We give a complete algebraic characterisation of amenable groups of isometries of X. For amenable discrete subgroups, an even narrower description is derived, implying Q-linearity in the…

Let $k$ be a field of characteristic $0$, $X$ be a geometrically connected, smooth and proper variety over $k$ and $x\in X(k)$ be a base point. Using the notion of iterated universal extensions, we show that Nori's fundamental group…

Using the Seiberg-Witten monopole equations, Baraglia recently proved that for most of simply-connected closed smooth $4$-manifolds $X$, the inclusions $\mathrm{Diff}(X) \hookrightarrow \mathrm{Homeo}(X)$ are not weak homotopy equivalences.…

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…

We study locally flat, compact, oriented surfaces in $4$-manifolds whose exteriors have infinite cyclic fundamental group. We give algebraic topological criteria for two such surfaces, with the same genus $g$, to be related by an ambient…

We prove a topological rigidity result for simple, thick, hyperbolic P-manifolds of dimension 2: isomorphism of the fundamental groups implies homeomorphism of the P-manifolds. An immediate application is a diagram rigidity theorem for…

We consider closed topological 4-manifolds $M$ with universal cover ${S^2\times{S^2}}$ and Euler characteristic $\chi(M) = 1$. All such manifolds with $\pi=\pi_1(M)\cong {\mathbb Z}/4$ are homotopy equivalent. In this case, we show that…

Understanding the relationships between geometry and topology is a central theme in Riemannian geometry. We establish two results on the fundamental groups of open (complete and noncompact) $n$-manifolds with nonnegative Ricci curvature and…

We consider the Euler characteristics $\chi(M)$ of closed orientable topological $2n$-manifolds with $(n-1)$-connected universal cover and a given fundamental group $G$ of type $F_n$. We define $q_{2n}(G)$, a generalized version of the…