Related papers: Codimension two souls and cancellation phenomena

We show that the topological conjugacy relation of diffeomorphisms on any manifold of dimension at least 2 is not classifiable by countable structures. This answers a question of Foreman and Gorodetski. We also prove that $E_0$ is reducible…

We prove a result analogous to Reeb's theorem in the context of Morse-Bott functions: if a closed, smooth manifold $M$ admits a Morse-Bott function having two critical submanifolds $S^k$ and $S^l$ ($k \neq l$), then $M$ has dimension…

We describe the topological structure of closed manifolds of dimension no less than four which admit Morse-Smale diffeomorphisms such that its non-wandering set contains any number of sink periodic points, and any number of source periodic…

We prove the existence of a geometric characteristic submanifold for non-positively curved manifolds of any dimension greater than or equal to three. In dimension three, our result is a geometric version of the topological characteristic…

Given an associative 3-fold in R^7 which is asymptotically conical with generic rate less than 1, we show that its moduli space of deformations is locally homeomorphic to the kernel of a smooth map between smooth manifolds. Moreover, the…

We describe a family of open subsets $M_A$ of the Moore plane, one for each subset $A$ of $\mathbb{R}$. Each of these subsets is a separable contractible (Hausdorff) 2-manifold, which is nonmetrizable if $A$ is uncountable. The collection…

One can define what it means for a compact manifold with corners to be a "contractible manifold with contractible faces." Two combinatorially equivalent, contractible manifolds with contractible faces are diffeomorphic if and only if their…

We prove:(1) the existence, for every integer n > 3, of a noncompact smooth n-dimensional topological manifold whose diffeomorphism group contains an isomorphic copy of every finitely presented group; (2) a finiteness theorem on finite…

Consider a codimension $1$ submanifold $N^n\subset M^{n+1}$, where $M^{n+1}\subset\mathbb{R}^{n+2}$ is a hypersurface. The envelope of tangent spaces of $M$ along $N$ generalizes the concept of tangent developable surface of a surface along…

2-stratifolds are a generalization of 2-manifolds in that there are disjoint simple closed curves where several sheets meet. They arise in the study of categorical invariants of 3-manifolds and may have applications to topological data…

Answering an old question, we find a domain X in the complex projective plane CP^2 which admits a strongly plurisubharmonic function, but such that every holomorphic function on X is constant. The domain X can be chosen diffeomorphic to an…

We call a closed, connected, orientable manifold in one of the categories TOP, PL or DIFF chiral if it does not admit an orientation-reversing automorphism and amphicheiral otherwise. Moreover, we call a manifold strongly chiral if it does…

We determine the homeomorphism (resp. diffeomorphism) types of those 2-connected 7-manifolds (resp. smooth 2-connected 7-manifolds) that admit regular circle actions (resp. smooth regular circle actions).

Special generic maps are higher dimensional versions of Morse functions with exactly two singular points, characterizing spheres topologically except $4$-dimensional cases: in these cases standard spheres are characterized. Canonical…

We prove a new rigidity result for an open manifold M with nonnegative sectional curvature whose soul S is odd-dimensional. Specifically, there exists a geodesic in S and a parallel vertical plane field along it with constant vertical…

In this article, we construct countably many mutually non-isotopic diffeomorphisms of some closed non simply-connected 4-manifolds that are homotopic to but not isotopic to the identity, by surgery along $\Theta$-graphs. As corollaries of…

An orientation-preserving recurrent homeomorphism of the two-sphere which is not the identity is shown to admit exactly two fixed points. A recurrent homeomorphism of a compact surface with negative Euler characteristic is periodic.

Let $Y$ be an algebraic manifold of dimension 3 with $H^i(Y, \Omega^j_Y)=0$ for all $j\geq 0$, $i>0$ and $h^0(Y, {\mathcal{O}}_Y) > 1$. Let $X$ be a smooth completion of $Y$ such that the boundary $X-Y$ is the support of an effective…

We study generic diffeomorphisms with a homoclinc class with non empty interior and in particular those admitting a codimension one dominated splitting. We prove that if in the finest dominated splitting the extreme subbundles are one…

A minifold is a smooth projective $n$-dimensional variety such that its bounded derived category of coherent sheaves $\D^b(X)$ admits a semi-orthogonal decomposition into an exceptional collection of $n+1$ exceptional objects. In this paper…