Related papers: Anomalous cw-expansive surface homeomorphisms

We prove the existence of finite groups of orientation-preserving homeomorphisms of some closed orientable surface $S$ that act freely and which extends as a group of homeomorphisms of some compact orientable $3$-manifold with boundary $S$,…

In this brief note, we show that there exist smooth 4-manifolds (with nonempty boundary) containing pairs of exotically knotted 2-spheres that remain exotic after one (either external or internal) stabilization. It follows that the ``one is…

We consider a closed convex set $C$ in a separable, infinite-dimensional Hilbert space and endow the set $\mathcal{N}(C)$ of nonexpansive self-mappings on $C$ with the topology of pointwise convergence. We introduce the notion of a somewhat…

Let f : X -> Y be a dominant polynomial mapping of affine varieties. For generic y in Y we have Sing(f^{-1}(y)) = f^{-1}(y) \cap Sing(X): As an application we show that symmetry defect hypersurfaces for two generic members of the…

This article follows and completes [arXiv:2511.14222], where we study the problem of bounded deviations for homeomorphisms of closed surfaces of genus $\ge 2$. This second part deals with bounded deviations relative to geodesic minimal…

We study the dynamics of planar diffeomorphisms having a unique fixed point that is a hyperbolic local saddle. We obtain sufficient conditions under which the fixed point is a global saddle. We also address the special case of…

Over the projective plane and at most two-step blowups of Hirzebruch surfaces, where there are strong full exceptional sequences of line bundles, we obtain foundational results about Gaeta resolutions of coherent sheaves by these line…

Wahl recently proved that the homology of the non-orientable mapping class group stabilizes as the genus increases. In this short note we analyse the situation where the underlying non-orientable surfaces have marked points.

In this paper, we prove that two normal complex surface germs that are inner bilipschitz--but not necessarily orientation-preserving--homeomorphic, have in fact the same oriented topological type and the same minimal plumbing graph. Along…

We point out that any stable generalized complex structure on a sphere bundle over a closed surface of genus at least two must be of constant type.

In this paper, we characterize closed incompressible surfaces of genus two in the complements of 3-bridge knots and links. This characterization includes that of essential 2-string tangle decompositions for 3-bridge knots and links.

Coboundary expansion (with $\mathbb{F}_2$ coefficients), and variations on it, have been the focus of intensive research in the last two decades. It was used to study random complexes, property testing, and above all Gromov's topological…

Under certain geometric condition, the surfaces in $\mathbb{C}^2$ with isolated CR singularity at the origin and with cubic lowest degree homogeneous term in its graph near the origin, can be reduced, up to biholomorphism of $\mathbb{C}^2$,…

In this paper, we study a two-parameter family of two-dimensional diffeomorphisms such that it has a cubic homoclinic tangency unfolding generically which is associated with a dissipative saddle point. Our first theorem presents an open set…

We consider compact minimal surfaces $f\colon M\to S^3$ of genus 2 which are homotopic to an embedding. We assume that the associated holomorphic bundle is stable. We prove that these surfaces can be constructed from a globally defined…

We introduce and study additive posets. We show that the top homology group (with coefficients in Z/2Z) of a finite dimensional CW-complex carries a structure of an additive poset invariant under subdivisions. Applications to CW-complexes…

Let $\pi\cln \cX\to S$ and $\pi\cln \cY\to S$ be two smooth families of projective non-uniruled manifolds over a Riemann surface $S$ (probably non-compact). Suppose these two families are pointwise isomorphic. We prove that there exists an…

We prove that local stable/unstable sets of homeomorphisms of an infinite compact metric space satisfying the gluing-orbit property always contain compact and perfect subsets of the space. As a consequence, we prove that if a positively…

We show that for a closed surface of genus at least 5, or a surface of genus at least 2 with at least one marked point, the set of uniquely ergodic foliations and the set of cobounded foliations is path-connected and locally path-connected.

In this paper we study local stable/unstable sets of sensitive homeomorphisms with the shadowing property defined on compact metric spaces. We prove that local stable/unstable sets always contain a compact and perfect subset of the space.…