arXiv research

Smooth $C^1$ contact maps are always smooth in rigid Carnot groups.

New smooth models for string groups defined in ∞-categories.

The study explores smooth structures on specific four-manifolds with cyclic groups, finding many admit infinitely many smooth structures.

New actions found on exotic spheres using group theory.

Study on 4-manifolds with exotic smooth structures and Z_2 fundamental group.

Smooth actions of cyclic groups on 3-manifolds are conjugate to smooth ones.

In this work we deal with coverings and actions of Lie group- groupoids being a sort of the structured Lie groupoids. Firstly, we define an action of a Lie group-groupoid on some Lie group and the smooth coverings of Lie group-groupoids. Later, we show the equivalence of the category of smooth actions of Lie group-grou…

Regular Lie groups are infinite dimensional Lie groups with the property that smooth curves in the Lie algebra integrate to smooth curves in the group in a smooth way (an `evolution operator' exists). Up to now all known smooth Lie groups are regular. We show in this paper that regular Lie groups allow to push surprisi…

The study finds smooth structures on specific 4-manifolds with even fundamental groups.

New smooth 2-group extensions from bundle gerbes on manifolds.

Book on infinite-dimensional Lie groups, covering basics and various classes.

Smooth actions of infinite groups linked to homotopy theory.

Smooth manifolds have equivalent diffeomorphism groups if and only if they are diffeomorphic.

Introduces Lie group actions in smoothing processes for currents and spaces with curvature.

New smooth structures found on certain 4D spaces.

Computes mapping class groups of 4-manifolds with boundary.

We show that every continuous action of a finite group on a smooth three-manifold is a uniform limit of smooth actions.

The paper studies gradings on nilpotent Lie algebras linked to smooth algebraic varieties.

New cohomology theory reveals $\mathbb{Q}/\mathbb{Z}$ in group homology.

The paper proves a smooth Birman-Hilden theorem for hyperkähler manifolds.

A trisection of a smooth, closed, oriented 4-manifold is a decomposition into three 4-dimensional 1-handlebodies meeting pairwise in 3-dimensional 1-handlebodies, with triple intersection a closed surface. The fundamental groups of the surface, the 3-dimensional handlebodies, the 4-dimensional handlebodies, and the clo…

The paper computes smooth structures on a specific product manifold.

Smooth surfaces in simply connected 4-manifolds yield groups with non-trivial homology.

Residually finite groups found in manifold automorphisms.

The paper generalizes a result on smooth mapping class groups and proves a property of Dehn twists in 4-manifolds.

Let $M^{2n}$ denote a closed $(n-1)$-connected smoothable topological $2n$-manifold. We show that the group $\mathcal{C}(M^{2n})$ of concordance classes of smoothings of $M^{2n}$ is isomorphic to the group of smooth homotopy spheres $\overlineΘ_{2n}$ for $n=4$ or $5$, the concordance inertia group $I_c(M^{2n})=0$ for $…

The abstract explores Artin presentations and their connection to 4-manifolds using triangle groups.

Novikov theorem extended to rational Pontryagin classes for cyclic group $C_4$.

The compact-open topology is minimal on diffeomorphism and homeomorphism groups of most smooth manifolds.

Smooth approximations for continuous functions on orbit spaces.

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 simple subgroups of diffeomorphism groups of compact smooth topological manifolds.

This work characterizes global quotient stacks---smooth stacks associated to a finite group acting a manifold---among smooth quotient stacks $[M/G]$, where $M$ is a smooth manifold equipped with a smooth proper action by a Lie group $G$. The characterization is described in terms of the action of the connected componen…

We define a new smooth concordance homomorphism based on the knot Floer complex and an associated concordance invariant, epsilon. As an application, we show that an infinite family of topologically slice knots are independent in the smooth concordance group.

The paper constructs infinitely many $G$-smoothings of a $G$-manifold.

New definite 4-manifolds found with non-cyclic groups.

We present reconstruction algorithms for smooth signals with block sparsity from their compressed measurements. We tackle the issue of varying group size via group-sparse least absolute shrinkage selection operator (LASSO) as well as via latent group LASSO regularizations. We achieve smoothness in the signal via fusion…

Study torsion-free nilpotent fundamental groups of smooth varieties up to rank 7.

We study Lie group structures on groups of the form C^\infty(M,K)}, where M is a non-compact smooth manifold and K is a, possibly infinite-dimensional, Lie group. First we prove that there is at most one Lie group structure with Lie algebra C^\infty(M,k) for which the evaluation map is smooth. We then prove the existen…

We produce infinite families of exotic actions of finite cyclic groups on simply connected smooth 4-manifolds with nontrivial Seiberg-Witten invariants.

In this paper we present another notion of a smooth manifold with corners and relate it to the commonly used concept in the literature. Afterwards we introduce complex manifolds with corners and show that if $M$ is a compact (respectively complex) manifold with corners and $K$ is a smooth (respectively complex) Lie gro…

The paper creates exotic 4-manifold structures with a specific group.

In this article, we study the smooth mapping class group of a surface S relative to a given Cantor set, that is the group of isotopy classes of orientation-preserving smooth diffeomorphisms of S which preserve this Cantor set. When the Cantor set is the standard ternary Cantor set, we prove that the subgroup consisting…

Let $M_1$ and $M_2$ be two $n$-dimensional smooth manifolds with boundary. Suppose we glue $M_1$ and $M_2$ along some boundary components (which are, therefore, diffeomorphic). Call the result $N.$ If we have a group $G$ acting continuously on $M_1,$ and also acting continuously on $M_2,$ such that the actions are comp…

Study finite group actions on exotic aspherical space forms.

On the basis of Brylinski's work, we introduce a notion of equivariant smooth Deligne cohomology group, which is a generalization of both the ordinary smooth Deligne cohomology and the ordinary equivariant cohomology. Using the cohomology group, we classify equivariant circle bundles with connection, and equivariant ge…

Smooth solutions found for hydrodynamic equations.

According to the work of Laitinen, Morimoto, Oliver and Pawałowski, a finite group $G$ has a smooth effective one fixed point action on some sphere if and only if $G$ is an Oliver group. For some finite Oliver groups $G$ of order up to $216$, and for $G=A_5\times C_n$ for $n=3,5,7$, we present a strategy of excluding o…

The paper proves residual finiteness of certain lattices and constructs surfaces with specific fundamental groups.