Related papers: Indices of vector fields and 1-forms
We construct a new category of vector spaces which contains both the standard category of vector spaces and Grassmannians. Its space of objects classifies vector bundles, its space of morphisms classifies bundle isomorphisms, and it can be…
We give a geometrical demonstration to the existence of holomorphic first integrals for certain kind of vector fields in $\mathbb{C}^2$ and $\mathbb{C}^3$.
Basic concepts of higher local fields and topologies on their additive and multiplicative groups are introduced.
A general type of ray class fields of global function fields is investigated. The systematic computation of their genera leads to new examples of curves over finite fields with comparatively many rational points.
We introduce a method to estimate the size of the domain of definition of the solutions of a meromorphic vector field on a neighborhood of its pole divisor. The corresponding techniques are, in a certain sense, quantitative versions of some…
The paper studies the complex 1-dimensional polynomial vector fields with real coefficients under topological orbital equivalence preserving the separatrices of the pole at infinity. The number of generic strata is determined, and a…
These are notes from an informal mini-course on factorization homology, infinity-categories, and topological field theories. The target audience was imagined to be graduate students who are not homotopy theorists.
Graph compositions generalize both integer compositions and partitions of a finite set. We develop formulas, generating functions and recurrence relations for composition counting functions for several families of graphs.
In an unpublished note [H1] we have described a method to obtain a formula for the index of an analytic vector field with (complex) isolated zero on a real analytic hypersurface with (complex) isolated singularity. This formula, like the…
Flows of vector fields are an essential tool in differential geometry, with countless applications in both theory and practice. While they have been extensively studied for ordinary manifolds and supermanifolds, a treatment of flows in…
We study the singularities of commuting vector fields of a real submanifold of a K\"ahler manifold $Z$.
We give a new and self-contained proof of the existence and unicity of the flow for an arbitrary (not necessarily homogeneous) smooth vector field on a real supermanifold, and extend these results to the case of holomorphic vector fields on…
In this paper we introduce the concept of generalized vector groupoid. Several properties of them are established.
We develop a theory of sesquilinear forms over finite fields, investigating their representations via polynomials and coefficient matrices, along with classification results for these forms. Through their connection to quadratic forms, we…
We consider shadowing properties for vector fields corresponding to different type of reparametrisations. We give an example of a vector field which has the oriented shadowing properties, but does not have the standard shadowing property.
We introduce a class of "Lipschitz horizontal" vector fields in homogeneous groups, for which we show equivalent descriptions, e.g. in terms of suitable derivations. We then investigate the associated Cauchy problem, providing a uniqueness…
This paper deals with valuations of fields of formal meromorphic functions and their residue fields. We explicitly describe the residue fields of the monomial valuations. We also classify all the discrete rank one valuations of fields of…
For a G-invariant holomorphic 1-form with an isolated singular point on a germ of a complex-analytic G-variety with an isolated singular point (G is a finite group) one has notions of the equivariant homological index and of the (reduced)…
We construct small models of number fields and deduce a better bound for the number of number fields of given degree and bounded discriminant.
An introductory overview of vector spaces, algebras, and linear geometries over an arbitrary commutative field is given. Quotient spaces are emphasized and used in constructing the exterior and the symmetric algebras of a vector space.…