Related papers: An anti-classification theorem for minimal homeomo…

A topological space is almost locally compact if it contains a dense locally compact subspace. We generalize a result from \cite{Ma}, showing that isomorphism on Borel classes of almost locally compact Polish metric structures is always…

We study surface representatives of homology classes of finite complexes which minimize certain complexity measures, including its genus and Euler characteristic. Our main result is that up to surgery at nullhomotopic curves minimizers are…

We prove that there does not exist any connected topological proper loop homeomorphic to a quasi-simple Lie group and having a compact Lie group as the group topologically generated by its left translations. Moreover, any connected…

We prove that while there are maps $\bT^4\to\#^3(\bS^2\times\bS^2)$ of arbitrarily large degree, there is no branched cover from $4$-torus to $\#^3(\bS^2\times \bS^2)$. More generally, we obtain that, as long as $N$ satisfies a suitable…

Let $\gamma$ be a pseudo-Anosov homeomorphism and $X$ an element of the Teichmuller space of a genus $g$ surface. In this paper, we find asymptotics for the number of pseudo-Anosov homeomorphisms that are conjugate to $\gamma$ and the axis…

We show that the classical homology theory of Steenrod may be enriched with descriptive set-theoretic information. We prove that the resulting definable homology theory provides a strictly finer invariant than Steenrod homology for compact…

Given a countable o-minimal theory T, we characterize the Borel complexity of isomorphism for countable models of T up to two model-theoretic invariants. If T admits a nonsimple type, then it is shown to be Borel complete by embedding the…

We show that the homotopy category of unpointed spaces admits no set of objects jointly reflecting isomorphisms by giving an explicit counterexample involving large symmetric groups. We also show that, in contrast, the spheres jointly…

We study the complexity of the classification problem of conjugacy on dynamical systems on some compact metrizable spaces. Especially we prove that the conjugacy equivalence relation of interval dynamical systems is Borel bireducible to…

Many non-locally compact second countable groups admit a comeagre conjugacy class. For example, this is the case for the automorphism group of the rational order and the automorphism group of the random graph [Truss]. A. Kechris and C.…

It is proved that there is no structure of left (right) cancelative semigroup on $[L]$-dimensional universal space for the class of separable compact spaces of extensional dimension $\le [L]$. Besides, we note that the homeomorphism group…

A topological space ${\mathcal X}$ is reversible iff each continuous bijection (condensation) $f: {\mathcal X} \rightarrow {\mathcal X}$ is a homeomorphism; weakly reversible iff whenever ${\mathcal Y}$ is a space and there are…

The homotopy type of the complement manifold of a complexified toric arrangement has been investigated by d'Antonio and Delucchi in a paper that shows the minimality of such topological space. In this work we associate to a given toric…

We prove that every topological conjugation between two germs of singular holomorphic curves in the complex plane is homotopic to another conjugation which extends homeomorphically to the exceptional divisors of their minimal…

We study the dynamics of Topologically Anosov homeomorphisms of non compact surfaces. In the case of surfaces of genus zero and finite type, we classify them. We prove that if $f:S \to S$, is a Topologically Anosov homeomorphism where $S$…

The paper deals with the program of determining the complexity of various homeomorphism relations. The homeomorphism relation on compact Polish spaces is known to be reducible to an orbit equivalence relation of a continuous Polish group…

The second author classified configurations of the singularities on tame sextics of torus type. In this paper, we give a complete classification of the singularities on irreducible sextics of torus type, without assuming the tameness of the…

We construct homeomorphisms of compacta from relations between finite graphs representing their open covers. Applied to the pseudoarc, this yields simple Fra\"iss\'e theoretic proofs of several important results, both old and new.…

Let $M$ be a closed surface. By $\Homeo(M)$ we denote the group of orientation preserving homeomorphisms of $M$ and let $\MC(M)$ denote the Mapping class group. In this paper we complete the proof of the conjecture of Thurston that says…

We prove that the complement of a toric arrangement has the homotopy type of a minimal CW complex. As a corollary we obtain that the integer cohomology of these spaces is torsion free. We use Discrete Morse Theory, providing a sequence of…