相关论文: Effective invariants of braid monodromy and topolo…

We introduce four invariants of algebraic varieties over imperfect fields, each of which measures either geometric non-normality or geometric non-reducedness. The first objective of this article is to establish fundamental properties of…

The aim of this work is to establish the existence of invariant manifolds in complex systems. Considering trajectory curves integral of multiple time scales dynamical systems of dimension two and three (predator-prey models, neuronal…

It is well known that plane curves with the same endpoints are homotopic. An analogous claim for plane curves with the same endpoints and bounded curvature still remains open. In this work we find necessary and sufficient conditions for two…

We study the equivariant concordance classes of two-bridge knots, providing an easy formula to compute their butterfly polynomial, and we give two different proofs that no two-bridge knot is equivariantly slice. Finally, we introduce a new…

In this paper, we prove that each automorphism of a surface braid group is induced by a homeomorphism of the underlying surface, provided that this surface is a closed, connected, orientable surface of genus at least 2, and the number of…

For affine algebraic plane curves we reduce a calculation of its invariants to calculation of the intersection of kernels of some derivations.

This is the paper as published. The topology of a complex plane curve singularity with real branches is deduced from any real deformation having delta crossings. An example of the computation of the global geometric monodromy of a…

We construct a topological invariant of algebraic plane curves, which is in some sense an adaptation of the linking number of knot theory. This invariant is shown to be a generalization of the I-invariant of line arrangements developed by…

A topological flux function is introduced to quantify the topology of magnetic braids: non-zero line-tied magnetic fields whose field lines all connect between two boundaries. This scalar function is an ideal invariant defined on a…

Analytic lattice cohomology is a new invariant of reduced curve singularities. In the case of plane curves, it is an algebro-geometric analogue of Heegaard Floer Link homology. However, by the rigidity of the analytic structure, lattice…

We explain how a version of Floer homology can be used as an invariant of symplectic manifolds with $b_1>0$. As a concrete example, we look at four-manifolds produced from braids by a surgery construction. The outcome shows that the…

Motivated by amplitude calculations in string theory we establish basic properties of homotopy invariant iterated integrals on affine curves.

In this paper, we address one of the most basic and fundamental problems in the theory of foliations and ODEs, the topological invariance of the algebraic multiplicity of a holomorphic foliation. For instance, we prove an adapted version of…

We give a criterion when a planar tree-like curve, i.e. a generic immersed plane curve each double point of which cuts it into two disjoint parts, can be send by a diffeomorphism of the plane onto a curve with no inflection points. We also…

We use classical invariant theory to solve the biholomorphic equivalence problem for two families of plane curve singularities previously considered in the literature. Our calculations motivate an intriguing conjecture that proposes a way…

We consider a map $F$ of class $C^r$ with a fixed point of parabolic type whose differential is not diagonalizable and we study the existence and regularity of the invariant manifolds associated with the fixed point using the…

Over a monoidal model category, under some mild assumptions, we equip the categories of colored PROPs and their algebras with projective model category structures. A Boardman-Vogt style homotopy invariance result about algebras over…

We numerically verify and analytically prove a winding number invariant that correctly predicts the number of edge states in one-dimensional, nearest-neighbor (between unit cells), two-band models with any complex couplings and open…

In the paper, we investigate properties of the nine-dimensional variety of the inflection points of the plane cubic curves. The description of local monodromy groups of the set of inflection points near singular cubic curves is given. Also,…

We study topological aspects of supersolvable abelian arrangements, toric arrangements in particular. The complement of such an arrangement sits atop a tower of fiber bundles, and we investigate the relationship between these bundles and…