arXiv research

We give examples of harmonic cellular maps between negatively curved manifolds which are not diffeomorphisms but are homotopic to diffeomorphisms.

Theta graph diffeomorphism shows nontrivial mapping class of 4-sphere.

Deformation quantization yields a new moment map on symplectic diffeomorphisms.

The study connects specific circle embeddings to 4-manifold diffeomorphisms.

New exotic 4D spaces with nontrivial mappings.

Study on mapping classes of real rational surface automorphisms, focusing on reducible maps and pseudo-Anosov maps.

A neural network method tackles high-dimensional diffeomorphic mapping problems.

Study the exponential map on surfaces using fluid dynamics.

New framework uses elliptic operators to study projective maps.

Proves surjectivity of certain smooth maps with non-properness sets.

Extends Palais' result on diffeomorphisms to homeomorphisms and bi-Lipschitz mappings.

The volume conjecture is extended for surface diffeomorphisms with quantum invariants.

We construct an infinite dimensional real analytic manifold structure for the space of real analytic mappings from a compact manifold to a locally convex manifold. Here a map is real analytic if it extends to a holomorphic map on some neighbourhood of the complexification of its domain. As is well known the constructio…

For a germ of a smooth map f and a subgroup G_V of any of the Mather groups G for which the source or target diffeomorphisms preserve some given volume form V in the source or in the target we study the G_V-moduli space of f that parameterizes the G_V-orbits inside the G-orbit of f. We find, for example, that this modu…

We prove that the Riemannian exponential map of the right-invariant $L^2$ metric on the group of volume-preserving diffeomorphisms of a two-dimensional manifold with a nonempty boundary is a nonlinear Fredholm map of index zero.

These lecture notes explain the geometry and discuss some of the analytical questions underlying image registration within the framework of large deformation diffeomorphic metric mapping (LDDMM) used in computational anatomy.

The abstract discusses the linear and smooth structures of mapping spaces.

The paper proves a factorization theorem for harmonic maps between Riemann surfaces and manifolds.

Let f:Σ_1 --> Σ_2 be an area preserving diffeomorphism between compact Riemann surfaces of constant curvature. The graph of f can be viewed as a Lagrangian submanifold in Σ_1\times Σ_2. This article discusses a canonical way to deform f along area preserving diffeomorphisms. This deformation process is realized through…

Study shows certain diffeomorphisms cannot be dynamically coherent.

Study geometric manifolds in arbitrary dimensions, focusing on maps and diffeomorphisms.

Smooth solutions found for hydrodynamic equations.

The affine diffeomorphism group $\mathrm{Aff}(S,q)$ of a half-translation surface $(S,q)$ comprise the self-diffeomorphisms with constant differential away from the singularities. This group coincides with the stabiliser of the associated Teichmüller disc under the action of the mapping class group on Teichmüller space…

An orientation preserving diffeomorphism over a surface embedded in a 4-manifold is called extendable, if this diffeomorphism is a restriction of an orientation preserving diffeomorphism on this 4-manifold. In this paper, we investigate conditions for extendability of diffeomorphisms over surfaces in the complex projec…

The paper studies exotic diffeomorphisms of 4-manifolds with b_+ = 2.

We classify up to conjugacy the group generated by a commuting pair of a periodic diffeomorphism and a hyperelliptic involution on an oriented closed surface. This result can be viewed as a refinement of Ishizaka's result on classification of the mapping classes of hyperelliptic periodic diffeomorphisms. As an applicat…

Registration, which aims to find an optimal 1-1 correspondence between shapes, is an important process in different research areas. Conformal mappings have been widely used to obtain a diffeomorphism between shapes that minimizes angular distortion. Conformal registrations are beneficial since it preserves the local ge…

Let K \subset Y be a knot in a three manifold which admits a longitude-framed surgery such that the surgered manifold has first Betti number greater than that of Y. We find a formula which computes the twisted Floer homology of the surgered manifold, in terms of twisted knot Floer homology. Using this, we compute the t…

Authors prove quantum invariant conjecture for figure-eight knot complement.

Generators of the 4-sphere's smooth mapping class group via diffeomorphisms of Montesinos twins.

Study local diffeomorphisms of conformal circles in pseudo-Riemannian manifolds.

Study on controllability and groups of manifolds with boundaries.

For the oriented 3-dimensional handlebody constructed from a 3-ball by attaching g 1-handles, it is shown that the natural surjection from the group of orientation preserving diffeomorphisms of it to the mapping class group of it has no section when g is at least 6.

For any smooth compact manifold $W$ of dimension at least two we prove that the classifying spaces of its group of diffeomorphisms which fix a set of $k$ points or $k$ embedded disks (up to permutation) satisfy homology stability. The same is true for so-called symmetric diffeomorphisms of $W$ connected sum with $k$ co…

Diffeomorphic Time Warping (DiffTW) is a novel method for time series classification that learns a diffeomorphic mapping between time series.

Study shows Hamiltonian diffeomorphisms form a connected component in $C^0$-topology for most symplectic rational surfaces.

Derivative map for disk diffeomorphisms induces nontrivial homotopy groups.

Deform moment map on symplectic connections using star product algebras.

Paper shows how scattering maps of Schrödinger equations relate to metrics.

Study Liouville action for harmonic maps between Riemann surfaces.

Let $M$ be a compact surface and $P$ be either $\mathbb{R}$ or $S^1$. For a smooth map $f:M\to P$ and a closed subset $V\subset M$, denote by $\mathcal{S}(f,V)$ the group of diffeomorphisms $h$ of $M$ preserving $f$, i.e. satisfying the relation $f\circ h = f$, and fixed on $V$. Let also $\mathcal{S}'(f,V)$ be its subg…

Study shows infinite order in mapping class groups for certain 3D shapes.

Exotic diffeomorphisms found on complex surfaces and 4-manifolds.

Embedding calculus proves convergence for surfaces.

Around 1960, R. Palais and J. Cerf proved a fundamental result relating spaces of diffeomorphisms and imbeddings of manifolds: If V is a submanifold of M, then the map from Diff(M) to Imb(V,M) that takes f to its restriction to V is locally trivial. We extend this and related results into the context of fibered manifol…

The study proves diffeomorphisms can be localized to simpler submanifolds.

Classifies $T^k$-manifolds with continuous sections.

We prove that any diffeomorphism of the sphere S^n to itself can be decomposed into bi-Lipschitz mappings of small isometric distortion and which move points a small amount in the spherical metric.