Related papers: Anomalous cw-expansive surface homeomorphisms

We classify invariant curves for birational surface maps that are expanding on cohomology. When the expansion is exponential, the arithmetic genus of an invariant curve is at most one. This implies severe constraints on both the type and…

We show that on a totally disconnected compact metric space every separating homeomorphisms is expansive except at periodic points. We conclude that minimal separating homeomorphisms are expansive and that every separating homeomorphism has…

We prove some general results concerning the size of the group of automorphisms of the Douady space of points on a surface. We then study some properties of the automorphisms coming from an automorphism of the surface, in particular their…

For a surface diffeomorphism, a compact invariant locally maximal set $W$ and some subset $A\subset W$ we study the $A$-exceptional set, that is, the set of points whose orbits do not accumulate at $A$. We show that if the Hausdorff…

Given an orientation-preserving and area-preserving homeomorphism $f$ of the sphere, we prove that every point which is in the common boundary of three pairwise disjoint invariant open topological disks must be a fixed point. As an…

The goal of the article is to characterize the conservative homeomorphisms of a closed orientable surface $S$ of genus $\geq 2$, that have finitely many periodic points. By conservative, we mean a map with no wandering point. As a…

This article deals with directional rotational deviations for non-wandering periodic point free homeomorphisms of the 2-torus which are homotopic to the identity. We prove that under mild assumptions, such a homeomorphism exhibits uniformly…

In this paper, we study Homeo$^1(S)$, the group of homeomorphisms of a surface that preserve the set of one-dimensional $C^1$ submanifolds of that surface. The group Homeo$^1(S)$ belongs to a family of similarly defined groups Homeo$^k(S)$…

Generalized topological spaces in the sense of Cs\'{a}sz\'{a}r have two main features which distinguish them from typical topologies. First, these families of subsets are not closed under intersections. Second, we allow for the possibility…

We show that invariant submanifolds with boundary, and more generally with corners which are normally expanded by an endomorphism are persistent as $a$-regular stratifications. This result will be shown in class $C^s$, for $s\ge 1$. We…

In this paper, we study non-wandering homeomorphisms of the two torus in the identity homotopy class, whose rotation sets are non-trivial line segments from $(0,0)$ to some totally irrational vector $(\alpha,\beta)$. We show this rotation…

We prove that cw-hyperbolic homeomorphisms with jointly continuous stable/unstable holonomies satisfy the periodic shadowing property and, if they are topologically mixing, the periodic specification property. We discuss difficulties to…

We study the surface of Gauss double points associated to a very general quartic surface and the natural morphisms associated to it.

We prove that for any orientable connected surface of finite type which is not a a sphere with at most four punctures or a torus with at most two punctures, any homeomorphism of the space of geodesic laminations of this surface, equipped…

Revised Version. An example of a locally smoothable stable surface that does not have a global smoothing has been added.

The Lefschetz fixed point theorem provides a powerful obstruction to the existence of minimal homeomorphisms on well-behaved spaces such as finite CW-complexes. We show that these obstructions do not hold for more general spaces. More…

We prove the existence of common fixed points for commuting homeomorphisms of the plane R^2 or the sphere S^2, which preserve a probability measure. For example: some commuting C^1-diffeomorphisms of S^2, which are sufficiently close to the…

We show that two closed, connected $4$-manifolds with finite fundamental groups are $\mathbb{CP}^2$-stably homeomorphic if and only if their quadratic $2$-types are stably isomorphic and their Kirby-Siebenmann invariant agrees.

We introduce and study the question how can stable birational types vary in a smooth proper family. Our starting point is the specialization for stable birational types of Nicaise and the author and our emphasis is on stable birational…

We show that the homeomorphism group of a surface without boundary does not admit a Hausdorff group topology strictly coarser than the compact-open topology. In combination with known automatic continuity results, this implies that the…