Related papers: Bi-rational maps in four dimensions with two invar…

This paper has a double goal, the first one is to make a slight survey of some theoretical results about the existence of positively invariant curves that allow to describe important properties of the set of bounded orbits and its boundary…

We study a new biholomorphic invariant of holomorphic maps between domains in different dimensions based on generic initial ideals. We start with the standard generic monomial ideals to find invariants for rational maps of spheres and…

We present novel results related to isomorphic resonance graphs of 2-connected outerplane bipartite graphs. As the main result, we provide a structure characterization for 2-connected outerplane bipartite graphs with isomorphic resonance…

We prove rigidity and gap theorems for self-dual and even Poincar\'e-Einstein metrics in dimension four. As a corollary, we give an obstruction to the existence of self-dual Poincar\'e-Einstein metrics in terms of conformal invariants of…

We study bipartite maps on the plane with one infinite face and one face of perimeter 2. At first we consider the problem of their enumeration an then study the connection between the combinatorial structure of a map and the degree of its…

We survey various classical results on invariants of polynomials, or equivalently, of binary forms, focussing on explicit calculations for invariants of polynomials of degrees 2, 3, 4.

We study certain extensions of the Adler map on Grassmann algebras $\Gamma(n)$ of order $n$. We consider a known Grassmann-extended Adler map, and assuming that $n=1$ we obtain a commutative extension of Adler's map in six dimensions. We…

In this paper, we introduce relative LS category of a map and study some of its properties. Then we introduce `higher topological complexity' of a map, a homotopy invariant. We give a cohomological lower bound and compare it with previously…

Previous works have been devoted to the study of two-dimensional noninvertible maps, obtained using a coupling between one-dimensional logistic maps. This paper is devoted to the study of a specific one, in order to complete previous…

We compute the oriented cobordism group of fold maps of 4-manifolds into the space with all the possible restrictions (and also with no restriction) to the singular fibers. We also give geometric invariants which describe completely the…

In contrast to the univariate case, several definitions are available for the notion of bounded variation for a bivariate function. This article is an attempt to study the Hausdorff dimension and box dimension of the graph of a continuous…

We use the classification of the quadrirational maps given by Adler, Bobenko and Suris to describe when such maps satisfy the Yang-Baxter relation. We show that the corresponding maps can be characterized by certain singularity invariance…

This work focuses on the degree bound of maps between balls with maximum geometric rank and minimum target dimension where this geometric rank occurs. Specifically, we show that rational proper maps between $\mathbb{B}_n$ and $\mathbb{B}_N$…

This paper has two parts. In the first one, we prove that an invariant dp-minimal type is either finitely satisfiable or definable. We also prove that a definable version of the (p,q)-theorem holds in dp-minimal theories of small or medium…

In this paper, we consider a class of continuous maps characterized by a singularity of order $x^{q/p}$ (with $p,q \in \mathbb{N}$, $p>q$, and $(p,q)=1$) on one side of the discontinuity boundary $\Sigma$ and a linear behaviour on the other…

In this series of papers, we propose a theory of enumerative invariants counting self-dual objects in self-dual categories. Ordinary enumerative invariants in abelian categories can be seen as invariants for the structure group $\mathrm{GL}…

We analyze a class of piecewise linear parabolic maps on the torus, namely those obtained by considering a linear map with double eigenvalue one and taking modulo one in each component. We show that within this two parameter family of maps,…

We give complete geometric invariants of cobordisms of fold maps with oriented singular set and cobordisms of even codimensional fold maps. These invariants are given in terms of cobordisms of stably framed manifolds and cobordisms of…

In this paper we revisit an integrable map of the plane which we obtained recently as a two-parameter family of deformed mutations in the cluster algebra of type D$_4$. The rational first integral for this map defines an invariant foliation…

Dimension four provides a peculiarly idiosyncratic setting for the interplay between scalar curvature and differential topology. Here we will explain some of the peculiarities of the four-dimensional realm via a careful discussion of the…