Related papers: On Distinguished local coordinates for locally hom…

We obtain sharp estimates on the connectivity of complex affine hypersurfaces in terms of the decomposition of the defining equation as a sum of weighted homogeneous components relative to some weight system.

We prove some restriction theorems for flat homogeneous surfaces of codimension greater than one.

We examine the $L^2$-topology of the gauge orbits over a closed Riemann surface. We prove a subtle local slice theorem based on the div-curl Lemma of harmonic analysis, and deduce local pathwise connectedness and local uniform…

This note gives the complete projective classification of rational, cuspidal plane curves of degree at least 6, and having only weighted homogeneous singularities. It also sheds new light on some previous characterizations of free and…

We investigate nicely embedded H--holomorphic maps into stable Hamiltonian three--manifolds. In particular we prove that such maps locally foliate and satisfy a no--first--intersection property. Using the compactness results of…

It is proved that no region of a homogeneous locally compact, locally connected metric space can be cut by an $F_\sigma$-subset of a "smaller" dimension. The result applies to different finite or infinite topological dimensions of…

Following the previous authors works (joint with I.A.Dynnikov) we develop a theory of the discrete analogs of the differential-geometrical (DG) connections in the triangulated manifolds. We study a nonstandard discretization based on the…

We prove that any holomorphic geometric structure of affine type on an Oeljeklaus- Toma manifold is locally homogeneous. For locally conformal K\"ahler Oeljeklaus-Toma manifolds we prove that all holomorphic geometric structures, and also…

This article presents families of 7-dimensional closed and simply-connected manifolds and fold maps on them such that squares of 2nd integral cohomology classes may not be divisible by 2. Fold maps are higher dimensional versions of Morse…

For a normal surface singularity, the discrepancy between the ordinary and dual middle-perversity intersection complexes over \(\mathbb Z\) is measured by a finite group \(E\). In previous work, \(E\) was identified with link torsion, the…

I demonstrate that the chart based approach to the study of the global structure of Lorentzian manifolds induces a homeomorphism of the manifold into a topological space as an open dense set. The topological boundary of this homeomorphism…

We interpret geometrically the torsion of the symmetric algebra of the ideal sheaf of a zero-dimensional scheme Z defined by $n+1$ equations in an $n$-dimensional variety. This leads us to generalise a formula of A.Dimca and S.Papadima in…

In 1995, S. Adams and G. Stuck as well as A. Zeghib independently provided a classification of non-compact Lie groups which can act isometrically and locally effectively on compact Lorentzian manifolds. In the case that the corresponding…

We construct explicit embeddings of generalized Danielewski surfaves in affine spaces. The equations defining these embeddings are obtained from the 2x2 minors of a matrix attached to a labelled rooted tree. Then we describe more precisely…

We discuss the extent to which solutions to one-phase free boundary problems can be characterized according to their topological complexity. Our questions are motivated by fundamental work of Luis Caffarelli on free boundaries and by…

We present a rigorous homogenization theorem for distributed dislocations. We construct a sequence of locally-flat Riemannian manifolds with dislocation-type singularities. We show that this sequence converges, as the dislocations become…

We give necessary conditions for the existence of a compact manifold locally modelled on a given homogeneous space, which generalize some earlier results, in terms of relative Lie algebra cohomology. Applications include both reductive and…

The authors study the geometry of lightlike hypersurfaces on manifolds $(M, c)$ endowed with a pseudoconformal structure $c = CO (n - 1, 1)$ of Lorentzian signature. Such hypersurfaces are of interest in general relativity since they can be…

We reconcile between two classical models of edge-dislocations in solids. The first model, dating from the early 1900s models isolated edge-dislocations as line singularities in locally-Euclidean manifolds. The second model, dating from the…

We revisit certain path-lifting and path-continuation properties of abstract maps as described in the work of F. Browder and R. Rheindboldt in 1950-1960s, and apply their elegant theory to exponential maps. We obtain thereby a number of…