Related papers: Smirnov-decompositions of vector fields
The evaluation of graphs on 2-spheres is a central ingredient of the Turaev-Viro construction of three-dimensional topological field theories. In this article, we introduce a class of graphs, called extruded graphs, that is relevant for the…
We prove that any diffeomorphism of the sphere S^n to itself can be decomposed into bi-Lipschitz mappings of small isometric distortion and which move points a small amount in the spherical metric.
We prove that a large family of graphs which are decomposable with respect to the modular decomposition can be reconstructed from their collection of vertex-deleted subgraphs.
We prove descent theorems for semiorthogonal decompositions using techniques from derived algebraic geometry. Our methods allow us to capture more general filtrations of derived categories and even marked filtrations, where one descends not…
It is proved the generalization of Toponogov theorem about the length of the curve in two-dimensional Riemannian manifolds in the case of two-dimensional Alexandrov spaces.
This short report establishes some basic properties of smooth vector fields on product manifolds. The main results are: (i) On a product manifold there always exists a direct sum decomposition into horizontal and vertical vector fields.…
The forms of surjective multiplicative isometries from the Smirnov class on the ball and the polydisk are given.
Several intrinsic topological ways to encode connections on vector bundles on smooth complex algebraic curves will be described. In particular the notion of {\em Stokes decompositions} will be formalised, as a convenient intermediate…
We give a simple proof of Dorronsoro's theorem and use similar ideas to establish an equivalence for embeddings of vector fields.
We use algebraic geometry over pointed monoids to give an intrinsic interpretation for the compactification of the spectrum of the ring of integers of a number field $K$, for the projective line over algebraic extensions of $\mathbb{F}_1$…
Recently we have obtained two simple proofs of Sharkovsky's theorem, one with directed graphs [7] and the other without [8]. In this note, we present yet more simple proofs of Sharkovsky's theorem.
Vector fields and line fields, their counterparts without orientations on tangent lines, are familiar objects in the theory of dynamical systems. Among the techniques used in their study, the Morse--Smale decomposition of a (generic) field…
We prove a semistable reduction theorem for principal bundles on curves in almost arbitrary characteristics. For exceptional groups we need some small explicit restrictions on the characteristic.
We complete the enumeration of the possible roots of the Alexander polynomial (both conventional and over finite fields) of a trigonal curve. The curves are not assumed proper or irreducible.
This note compares the usual (absolute) Gromov-Witten invariants of a symplectic manifold with the invariants that count the curves relative to a (symplectic) divisor D. We give explicit examples where these invariants differ even though it…
We classify stably simple reducible curve singularities in complex spaces of any dimension. This extends the same classification of of irreducible curve singularities obtained by V.I.Arnold. The proof is essentially based on the method of…
We give a proof of the Gromov compactness theorem using the language of stable curves (i.e. cusp-curve of Gromov, or stable maps of Kontsevich and Manin) in general setting: An almost complex structure on a target manifold is only…
A discussion of recent work of C.Demeter, L.Guth and the author of the proof of the Vinogradov Main Conjecture using the decoupling theory for curves
Degenerations of Lie algebras of meromorphic vector fields on elliptic curves (i.e. complex tori) which are holomorphic outside a certain set of points (markings) are studied. By an algebraic geometric degeneration process certain…
In this paper, we extend the method developed in [17, 18] to curves in the Minkowski plane. The method proposes a way to study deformations of plane curves taking into consideration their geometry as well as their singularities. We deal in…