Related papers: A short proof of smooth implies flat
The purpose of this note is to rephrase Speyer's elegant topological proof for Kasteleyn's Theorem in a simple graph theoretical manner.
We survey results devoted to the lattice of varieties of monoids. Along with known results, some unpublished results are given with proofs. A number of open questions and problems are also formulated.
In this note, simple proofs of certain well-known results involving the positive square root of positive matrices are given.
In this paper we discuss the smoothness conditions for metrics on a cohomogeneity one manifold, i.e. metrics invariant under a Lie group whose generic orbits are hypersurfaces. Along these hypersurfaces one describes the metrics in terms of…
In this paper we consider strata of flat metrics coming from quadratic differentials (semi-translation structures) on surfaces of finite type. We provide a necessary and sufficient condition for a set of simple closed curves to be…
This is a short expository account of the regularity lemma for stable graphs proved by the authors, with some comments on the model theoretic context, written for a general logical audience.
It is proved that the degree of a morphism from a smooth projective n-fold with Picard number one to a smooth n-quadric is bounded (provided, of course, that n is at least three). Actually it has been proved some years ago, but I have never…
We prove an improvement of flatness result for nonlocal minimal surfaces which is independent of the fractional parameter $s$ when $s\rightarrow 1^-$. As a consequence, we obtain that all the nonlocal minimal cones are flat and that all the…
We show that given a dominant morphism between two smooth varieties of the same dimension, the induced morphism between the formal neighborhoods of two arcs on these varieties is a closed embedding, of codimension given by the order of…
We prove equivalent numerical conditions for a complete spherical variety to admit a toric structure, and for the smoothness of an arbitrary spherical variety along any given G-orbit. The conditions are in terms of spherical skeletons, a…
In [Mor], we have introduced a notion of flat laminations on surfaces endowed with a flat structure, similar to geodesic laminations on hyperbolic surfaces. Here is a sequel to this article that aims at defining transversal measures on flat…
A graph G on omega_1 is called <omega-smooth if for each uncountable subset W of omega_1, G is isomorphic to G[W-W'] for some finite W'. We show that in various models of ZFC if a graph G is <omega-smooth then G is necessarily trivial, i.e,…
On a compact, oriented, Riemannian manifold, the Hodge decomposition theorem associates a smooth primitive to any exact smooth form omega. In this paper, we show that given a smooth family of exact smooth forms omega(t), the family of…
We introduce the notion of approximate smoothness in a normed linear space. We characterize this property and show the connections between smoothness and approximate smoothness for some spaces. As an application, we consider in particular…
We provide an alternative, simpler proof of the existence of thick triangulations for noncompact $\mathcal{C}^1$ manifolds. Moreover, this proof is simpler than the original one given in \cite{pe}, since it mainly uses tools of elementary…
A Lie algebroid on a variety X/k is an extension \alpha: g_X \to T_X of the tangent sheaf both as O_X-module and Lie algebra over the base field, with the obvious compatibilities; and given a Lie algebroid one has its associated ring of…
The Dold$-$Thom theorem states that for a sufficiently nice topological space, M, there is an isomorphism between the homotopy groups of the infinite symmetric product of M and the homology groups of M itself. The crux of most known proofs…
We show that every smooth manifold admits a smooth triangulation transverse to a given smooth map. This removes the properness assumption on the smooth map used in an essential way in Scharlemann's construction [5].
We show that a rational holonomy representation of any flat manifold except torus must have at least two non-equivalent irreducible subrepresentations. As an application we show that if a K\"ahler flat manifold is not a torus then its…
This note presents an elementary and direct proof for the convexity of the Choquet integral when the corresponding set function is submodular.