Related papers: $C^\infty$-manifolds with skeletal diffeology

The gauge symmetry of classical general relativity under space-time diffeomorphisms implies that any path integral quantization which can be interpreted as a sum over space-time geometries, gives rise to a formal invariant of smooth…

For a compact, smooth C^r orbifold (without boundary), we show that the topological structure of the orbifold diffeomorphism group is a Banach manifold for finite r \ge 1 and a Frechet manifold if r=infty. In each case, the local model is…

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…

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…

Our main result asserts that for any given numbers C and D the class of simply connected closed smooth manifolds of dimension m<7 which admit a Riemannian metric with sectional curvature bounded in absolute value by C and diameter uniformly…

Let $(M,g)$ be a $C^\infty$-smooth, $n$-dimensional Riemannian manifold which is diffeomorphic to $\RR^n$ and admit an action of a properly discontinuous and cocompact group. This work proves the existence of a $C^\infty$ equivariant…

In this article, we establish the Drinfeld correspondence between Poisson Lie groups and their infinitesimal counterparts, Lie bialgebras, in the infinite-dimensional setting. Specifically, we extend this correspondence to regular Lie…

In this note we describe a family of arguments that link the homotopy-type of a) the diffeomorphism group of the disc $D^n$, b) the space of co-dimension one embedded spheres in a sphere and c) the homotopy-type of the space of co-dimension…

Topological classification of even the simplest Morse-Smale diffeomorphisms on 3-manifolds does not fit into the concept of singling out a skeleton consisting of stable and unstable manifolds of periodic orbits. The reason for this lies…

For each integer q>0 there is a cohomology theory such that the zero cohomology group of a manifold N of dimension n is a certain group of cobordism classes of proper fold maps of manifolds of dimension n+q into N. We prove a splitting…

On an open, connected symplectic manifold $(M,\omega)$, the group of Hamiltonian diffeomorphisms forms an infinite-dimensional Fr\'echet Lie group with Lie algebra $C^{\infty}_c(M)$ and adjoint action given by pullbacks. We prove that this…

We classify up to diffeomorphism all smooth manifolds homeomorphic to the complex projective m-space $\mathbb{C}P^{m}$ for $m = 5, 6, 7$ and $8$. As an application, for $m = 7$ and $8$, we compute the smooth tangential structure set of…

Kontsevich conjectured that $\text{BDiff}(M, \text{rel }\partial)$ has the homotopy type of a finite CW complex for all compact $3$-manifolds with non-empty boundary. Hatcher-McCullough proved this conjecture when $M$ is irreducible. We…

Given a closed smooth four-dimensional manifold, we construct a diffeomorphism that has a homoclinic class whose continuation locally generically satisfies the following condition: it does not admit any kind of dominated splittings whereas…

In this paper, we study diffeological spaces as certain kinds of discrete simplicial presheaves on the site of cartesian spaces with the coverage of good open covers. The \v{C}ech model structure on simplicial presheaves provides us with a…

We establish that if a submanifold $M$ of $\mathbb{R}^n$ is definable in some o-minimal structure then any definable submanifold $N\subset \mathbb{R}^n$ which is $\mathscr{C}^\infty$ diffeomorphic to $M$, with a diffeomorphism $h:N\to M$…

The $\pi_2$-diffeomorphism finiteness result (\cite{FR1,2}, \cite{PT}) asserts that the diffeomorphic types of compact $n$-manifolds $M$ with vanishing first and second homotopy groups can be bounded above in terms of $n$, and upper bounds…

The existence of a model structure on the category $\mathcal{D}$ of diffeological spaces is crucial to developing smooth homotopy theory. We construct a compactly generated model structure on the category $\mathcal{D}$ whose weak…

We prove that the monodromy diffeomorphism of a complex 2-dimensional isolated hypersurface singularity of weighted-homogeneous type has infinite order in the smooth mapping class group of the Milnor fiber, provided the singularity is not a…

Diffeomorphism groups $G$ of manifolds $M$ on locally $\bf F$-convex spaces over non-Archimedean fields $\bf F$ are investigated. It is shown that their structure has many differences with the diffeomorphism groups of real and complex…