Related papers: Aspherical 4-Manifolds, Complex Structures, and Ei…

Let (M, g, omega) be a compact, almost-Kaehler Einstein 4-manifold of negative star-scalar curvature. Then (M, omega) is a MINIMAL symplectic 4-manifold of general type. In particular, M cannot be differentiably decomposed as a connected…

In this paper, a lot of examples of four-dimensional manifolds with an almost hypercomplex pseudo-Hermitian structure are constructed in several explicit ways. The received 4-manifolds are characterized by their linear invariants in the…

D. D. Long and A. W. Reid have shown that some compact flat 3-manifold cannot be diffeomorphic to a cusp cross-section of any complete finite volume 1-cusped real hyperbolic 4-manifold. This note concerns the complex hyperbolic case. We…

We show that if a compact, oriented 4-manifold admits a coassociative-free immersion into the Euclidean 7-space then its Euler characteristic and signature vanish. Moreover, in the spin case the Gauss map is contractible, so that the…

We define a renormalized characteristic class for Einstein asymptotically complex hyperbolic (ACHE) manifolds of dimension 4: for any such manifold, the polynomial in the curvature associated to the characteristic class euler-3signature is…

We introduce a new generalization of Gompf nuclei and give applications. We construct infinitely many exotic smooth structures for a large class of compact 4-manifolds with boundary, regarding topological invariants. We prove that a large…

We classify the possible elementary amenable fundamental groups of compact aspherical 4-manifolds with boundary and conclude that they are either polycyclic or solvable Baumslag- Solitar. Since these groups are good and satisfy the…

We classify nilpotent Lie algebras with complex structures of weakly non-nilpotent type in real dimension eight, which is the lowest dimension where they arise. Our study, together with previous results on strongly non-nilpotent structures,…

We construct examples of four dimensional manifolds with Spin$^c$-structures, whose moduli spaces of solutions to the Seiberg-Witten equations, represent a non-trivial bordism class of positive dimension, i.e. the Spin$^c$-structures are…

We study the topology of closed, simply-connected, 6-dimensional Riemannian manifolds of positive sectional curvature which admit isometric actions by $SU(2)$ or $SO(3)$. We show that their Euler characteristic agrees with that of the known…

We show that every closed symplectic four-dimensional manifold admits compatible almost Kaehler metrics of negative scalar curvature.

Almost hypercomplex manifolds with Hermitian and Norden metrics and more specially the corresponding quaternionic Kaehler manifolds are considered. Some necessary and sufficient conditions the investigated manifolds be isotropic…

We prove that compact quaternionic-K\"ahler manifolds of positive scalar curvature admit no almost complex structure, even in the weak sense, except for the complex Grassmannians $Gr_2(C^{n+2})$. We also prove that irreducible inner…

This paper is concerned with the construction of special metrics on non-compact 4-manifolds which arise as resolutions of complex orbifold singularities. Our study is close in spirit to the construction of the hyperkaehler gravitational…

It is well-known that odd-dimensional manifolds have Euler characteristic zero. Furthemore orientable manifolds have an even Euler characteristic unless the dimension is a multiple of $4$. We prove here a generalisation of these statements:…

We formulate a conjecture relating the topology of a manifold's universal cover with the existence of metrics with positive $m$-intermediate curvature. We prove the result for manifolds of dimension $n\in\{3,4,5\}$ and for most choices of…

We discuss the Euclidean limit of hyperbolic SU(2)-monopoles, framed at infinity, from the point of view of pluricomplex geometry. More generally, we discuss the geometry of hypercomplex manifolds arising as limits of pluricomplex…

The purpose of this article is twofold. First we outline a general construction scheme for producing simply-connected minimal symplectic 4-manifolds with small Euler characteristics. Using this scheme, we illustrate how to obtain…

For any given finitely presented group G there exists a closed oriented 4-manifold with fundamental group G. What pairs of integers can occur as the signature and Euler characteristic of such a 4-manifold? The first part of this paper…

We exhibit a closed aspherical 5-manifold of nonpositive curvature that fibers over a circle whose fundamental group is hyperbolic relative to abelian subgroups such that the fiber is a closed aspherical 4-manifold whose fundamental group…