Related papers: Piecewise linear homeomorphisms of the real line
Real Clifford algebras for arbitrary number of space and time dimensions as well as their representations in terms of spinors are reviewed and discussed. The Clifford algebras are classified in terms of isomorphic matrix algebras of real,…
The dimension of spaces of global sections for line bundles on semistable curves parametrized by the compactified Picard scheme is studied. The theorem of Riemann is shown to hold. The theorem of Clifford is shown to hold in the following…
We derive a piecewise-linear formula for the rigid representation of a Dynkin quiver of a given dimension vector, and illustrate the formula in several examples.
We study the linearization problem of germs of holomorphic diffeomorphisms with resonant linear part. The formal linearization requires in general an infinite number of algebraic relations to be satisfied by the coefficients of the power…
We give a simple analytic criterion which characterizes linearizable 1-codimensional webs. Then we give an invariant geometrical interpretation of it, in term of projective connection. We explain then how our approach allows to study…
In this study, we introduce the notion of $PL_\delta$-homeomorphisms of $\mathbb{R}^n$. Furthermore, we provide a combinatorial criterion reliant on the vertices and edges of simplicial structures, to determine whether a piecewise-linear…
Let $g:\, [0, 1]\rightarrow [0, 1]$ be piecewise linear unimodal map. We say that $g$ has non-trivial piecewise linear commutator, if there is a continuous piecewise linear $\psi:\, [0, 1]\rightarrow [0, 1]$ such that $g\circ \psi =…
The tempered representations of a real reductive Lie group $G$ are naturally partitioned into series associated with conjugacy classes of Cartan subgroups $H$ of $G$. We define partial Dirac cohomology, apply it for geometric construction…
Following our previous work, we develop an algorithm to compute a presentation of the fundamental group of certain partial compactifications of the complement of a complex arrangement of lines in the projective plane. It applies, in…
In this work we study the following realization problem: given a piecewise homeomorphism $\Phi: S^1 \rightarrow S^1$, which geometrical and dynamical conditions on $\Phi$ are sufficient to realize it as a Bowen-Series-like map associated to…
We give a geometric approach to the relation between the irreducible components of the characteristic varieties of local systems on a plane curve arrangement complement and the associated pencils of plane curves discovered recently by M.…
We explore the relation of weak conjugacy in the group of homeomorphisms isotopic to the identity, for surfaces.
Group classification of a class of nonlinear fin equations is carried out exhaustively. Additional equivalence transformations and conditional equivalence groups are also found. They allow to simplify results of classification and further…
Our paper develops a theory of Poisson slices and a uniform approach to their partial compactifications. The theory in question is loosely comparable to that of symplectic cross-sections in real symplectic geometry.
Let $\H^{n+1}$ denote the $n + 1$-dimensional (real) hyperbolic space. Let $\s^{n}$ denote the conformal boundary of the hyperbolic space. The group of conformal diffeomorphisms of $\s^n$ is denoted by $M (n)$. Let $M_o (n)$ be its identity…
We present an algorithm to express Wilson lines that are defined on piecewise linear paths in function of their individual segments, reducing the number of diagrams needed to be calculated. The important step lies in the observation that…
The rational homology group of the order complex of non-even partitions of a finite set is calculated. A twisted version of the Goresky-MacPherson approach to similar homology calculations is proposed.
A simple method called symbolic representation for piecewise linear functions on the real line is introduced and used to compute the numbers of periodic points of all periods for some such functions. Since, for every positive integer m, the…
We identify the complexity of the classification problem for automorphisms of a given countable regularly branching tree up to conjugacy. We consider both the rooted and unrooted cases. Additionally, we calculate the complexity of the…
We classify, up to isomorphism and up to equivalence, division gradings (by abelian groups) on finite-dimensional simple real algebras. Gradings on finite-dimensional simple algebras are determined by division gradings, so our results give…