Related papers: Non-formal compact manifolds with small Betti numb…

In this paper we discuss face numbers of generalised triangulations of manifolds in arbitrary dimensions. This is motivated by the study of triangulations of simply connected $4$-manifolds: We observe that, for a triangulation $\mathcal{T}$…

Let $M$ be a closed, oriented, connected 3--manifold and $(B,\pi)$ an open book decomposition on $M$ with page $\Sigma$ and monodromy $\varphi$. It is easy to see that the first Betti number of $\Sigma$ is bounded below by the number of…

We prove a Bonnet-Myers type theorem for quaternionic contact manifolds of dimension bigger than 7. If the manifold is complete with respect to the natural sub-Riemannian distance and satisfies a natural Ricci-type bound expressed in terms…

We prove the existence of Sasakian metrics with positive Ricci curvature on certain highly connected odd dimensional manifolds. In particular, we show that manifolds homeomorphic to the 2k-fold connected sum of S^{2n-1} x S^{2n} admit…

We present the census of all non-orientable, closed, connected 3-manifolds admitting a rigid crystallization with at most 30 vertices. In order to obtain the above result, we generate, manipulate and compare, by suitable computer…

Given a closed oriented PL four-manifold $X$ and a closed surface $B$ embedded in $X$ with isolated cone singularities, we give a formula for the signature of an irregular dihedral cover of $X$ branched along $B$. For $X$ simply-connected,…

The possibilities for new or unusual kinds of topological, locally linear periodic maps of non-prime order on closed, simply connected 4-manifolds with positive definite intersection pairings are explored. On the one hand, certain…

We discuss the geometry of some arithmetic orbifolds locally isometric to a product of real hyperbolic spaces of dimension two and three, and prove that certain sequences of non-uniform orbifolds are convergent to this space in a geometric…

We classify closed, simply-connected non-negatively curved 5-manifolds admitting an (almost) effective, isometric $T^3$ or $T^2$ action. As a direct consequence, we show that for any manifold, of dimensions up to and including 9 under the…

In 2017, Qiao and Koolen showed that for any fixed integer $D\geq 3$, there are only finitely many such graphs with $\theta_{\min}\leq -\alpha k$, where $0<\alpha<1$ is any fixed number. In this paper, we will study non-bipartite…

We prove a nilpotency theorem for the Bauer-Furuta stable homotopy Seiberg-Witten invariants for smooth closed 4-manifolds with trivial first Betti number.

We study the possibility of realizing exotic smooth structures on punctured simply connected $4$-manifolds as leaves of a codimension one foliation on a compact manifold. In particular, we show the existence of uncountably many smooth open…

We provide examples of contact manifolds of any odd dimension $\geq 5$ which are not diffeomorphic but have exact symplectomorphic symplectizations.

We show that closed manifolds supporting a nonpositively curved metric with negative $([\frac{n}{4}]+1)$-Ricci curvature, have positive simplicial volume. This answers a special case of a conjecture of Gromov.

The Betti numbers are fundamental topological quantities that describe the k-dimensional connectivity of an object: B_0 is the number of connected components and B_k effectively counts the number of k-dimensional holes. Although they are…

We prove the following result: Let $(M,g_0)$ be a complete noncompact manifold of dimension $n\geq 12$ with isotropic curvature bounded below by a positive constant, with scalar curvature bounded above, and with injectivity radius bounded…

We show that noncompact simply connected harmonic manifolds with volume density $\Theta_{p}(r) =\sinh ^{n-1} r$ is isometric to the real hyperbolic space and noncompact simply connected K\"{a}hler harmonic manifold with volume density…

We are interested in the maximal values of the Betti numbers b_i({\mathbb R}X_m^n) for fixed i,m,n; where {\mathbb R}X_m^n is the real part of a real nonsingular hypersurface of degree m in the complex projective space {\mathbb C}P^n, and…

It is proved that the moduli space of all connected compact orientable embedded minimal affine Lagrangian submanifolds of a complex equiaffine space constitutes an infinite dimensional Frechet manifold (if it is not the empty set). The…

We study the asymptotics of the number N(t) of geometrically distinct closed geodesics of a Riemannian or Finsler metric on a connected sum of two compact manifolds of dimension at least three with non-trivial fundamental groups and apply…