This paper is concerned with the problem of approximating a homeomorphism by piecewise affine homeomorphisms. The main result is as follows: every homeomorphism from a planar domain with a polygonal boundary to R that is globally Hölder continuous of exponent α ∈ (0, 1], and whose inverse is also globally Hölder continuous of exponent α can be approximated in the Hölder norm of exponent β by pi...

This is a glossary of notions and methods related with the topological theory of collections of affine planes, including braid groups, configuration spaces, order complexes, stratified Morse theory, simplicial resolutions, complexes of graphs, Orlik– Solomon rings, Salvetti complex, matroids, Spanier–Whitehead duality, twisted homology groups, monodromy theory and multidimensional hypergeometri...

We consider actions of the free semigroup with two generators on the real line, where the generators act as affine maps, one contracting and one expanding, with distinct fixed points. Then every orbit is dense in a half-line, which leads to the question whether it is, in some sense, uniformly distributed. We present answers to this question for various interpretations of the phrase “uniformly d...

In this paper we show that expansion of a Buchsbaum simplicial complex is $CM_t$, for an optimal integer $tgeq 1$. Also, by imposing extra assumptions on a $CM_t$ simplicial complex, we provethat it can be obtained from a Buchsbaum complex.

‎In this paper we prove that a simplicial complex is determined‎ ‎uniquely up to isomorphism by its barycentric subdivision as well as‎ ‎its comparability graph‎. ‎We also put together several algebraic‎, ‎combinatorial and topological invariants of simplicial complexes‎.

We study semigroup C*-algebras of ax + b-semigroups over integral domains. The goal is to generalize several results about C*-algebras of ax + bsemigroups over rings of algebraic integers. We prove results concerning K-theory and structural properties like the ideal structure or pure infiniteness. Our methods allow us to treat ax+b-semigroups over a large class of integral domains containing al...

Let X be an algebraic variety, the set of points where X is not Cohen-Macaulay is the Non-CohenMacaulay locus, this set was study in [1]. Macaulayfication is an analogous operation to resolution of singularities and was considered in [7] where the main theorem of Macaulayfication is given. For any affine semigroup (without torsion) S ⊂ IN let G(S) be the subgroup of ZZ generated by S and S̄ be t...