Related papers: Smooth perfectness for the group of diffeomorphism…

We give a uniform construction that, on input of a recursive presentation $P$ of a group, outputs a recursive presentation of a torsion-free group, isomorphic to $P$ whenever $P$ is itself torsion-free. We use this to re-obtain a known…

We prove that every suitable $4$-manifold with $b_1=0$ and with an embedded Riemann surface of genus $2$ is of simple type. We find a relationship between the basic classes of two of these $4$-manifolds and those of the connected sum along…

For a given coorientable contact manifold $(M^{2n+1},\xi)$, we consider the group $ \operatorname{Cont}_c^{(r,\delta)}(M,\alpha)$ consisting of $C^{r,\delta}$ contactomorphisms with compact support which is equipped with…

We give a new proof that compact infra-solvmanifolds with isomorphic fundamental groups are smoothly diffeomorphic. More generally, we prove rigidity results for manifolds which are constructed using affine actions of virtually polycyclic…

A topological group G is h-complete if every continuous homomorphic image of G is (Raikov-)complete; we say that G is hereditarily h-complete if every closed subgroup of G is h-complete. In this paper, we establish open-map properties of…

We give a simple proof on the Poincar\'e's conjecture which states that every compact smooth $3-$manifold which is homotopically equivalent to $S^3$ is diffeomorphic to $S^3$.

Let f be a class P -homeomorphism of the circle. We prove that there exists a piecewise analytic homeomorphism that conjugate f to a one-class P with prescribed break points lying on pairwise distinct orbits. As a consequence, we give a…

Conjugation spaces relate the cohomology of a space and its fixed points via a degree-halving isomorphism and admit a characterization in terms of homological purity. We extend this framework to the Klein four group, where the corresponding…

In this note we prove that a homomorphism from a compact connected simple Lie group with the norm topology to any separable SIN group is automatically continuous. This generalizes a result by Dowerk and Thom. Further, we prove some…

In this paper we introduce perfectly supportable semigroups and prove that they are \sigma-discrete in each Hausdorff shift-invariant topology. The class of perfectly supportable semigroups includes each subsemigroup S of the semigroup…

We study the class of norms on the space of smooth functions on a closed symplectic manifold, which are invariant under the action of the group of Hamiltonian diffeomorphisms. Our main result shows that any such norm that is continuous with…

If $(X, \omega)$ is a symplectic manifold, and $\Sigma$ is a smooth symplectic submanifold Poincar\'e dual to a positive multiple of $\omega$, $X \setminus \Sigma$ admits a compactification as a Liouville domain, which we then complete to…

In this paper we give a full diffeomorphism characterization of compact simply connected cohomogeneity one manifolds in dimension six.

Let $\mathfrak{C}$ be some Cantor space. We study groups of homeomorphisms of $\mathfrak{C}$ which are vigorous, or, which are flawless, where we introduce both of these terms here. We say a group $G\leq \operatorname{Homeo}(\mathfrak{C})$…

Given a compact surface $M$, consider the natural right action of the group of diffeomorphisms $\mathcal{D}(M)$ of $M$ on $\mathcal{C}^{\infty}(M,\mathbb{R})$ defined by the rule: $(f,h)\mapsto f\circ h$ for $f\in…

If $G$ is a finitely generated group with generators $\{g_1,..., g_s\}$, we say an infinite-order element $f \in G$ is a distortion element of $G$ provided that $\displaystyle \liminf_{n \to \infty} \frac{|f^n|}{n} = 0$, where $|f^n|$ is…

The density property for a Stein manifold X implies that the group of holomorphic diffeomorphisms of X is infinite-dimensional and, in a certain well-defined sense, as large as possible. We prove that if G is a complex semisimple Lie group…

To construct an $A_{\infty}$-form for a loop space in the category of diffeological spaces, we have two minor problems. Firstly, the concatenation of paths in the category of diffeological spaces needs a small technical trick (see…

A finite group is said to have "perfect order classes" if the number of elements of any given order is either zero or a divisor of the order of the group. The purpose of this note is to describe explicitly the finite Hamiltonian groups with…

We give constraints on smooth families of 4-manifolds with boundary using Manolescu's Seiberg-Witten Floer stable homotopy type, provided that the fiberwise restrictions of the families to the boundaries are trivial families of 3-manifolds.…