Constructs pseudo-isotopies with Cerf diagrams and Hatcher-Wagoner invariants for barbell maps.
problem Understanding and constructing pseudo-isotopies for barbell maps.
method Constructs specific pseudo-isotopies with Cerf diagrams and Hatcher-Wagoner invariants.
result Every pseudo-isotopy with vanishing first Hatcher-Wagoner invariant can be isotoped to a composition of standard barbell pseudo-isotopies.
The paper shows how certain circle families in S1imesD3 relate to sphere families in S2imesD2 and induces nontrivial barbell diffeomorphisms.
problem Understanding the relationship between circle and sphere families in specific 3-manifolds.
method Analyzing the fundamental groups and ambient extensions of circle and sphere families.
result Induces nontrivial barbell diffeomorphisms of S1imesS2imesI. The paper constructs many knotted and linked objects in higher dimensions.
problem Understanding knotted and linked objects in higher dimensions.
method Using barbell diffeomorphisms to construct examples.
result Infinitely many knotted and linked objects in 4 and 5 dimensions.
New invariant detects more elements in 4D diffeomorphism group.
problem Detecting more elements in the mapping class group of 4D handlebodies.
method Defined and computed a new invariant (W3)m for π0Diff(aturalmS1imesD3,∂). result Infinitely many non-isotopic separating 3-balls found.
The study connects specific circle embeddings to 4-manifold diffeomorphisms.
problem Understanding diffeomorphisms of 4-manifolds from specific circle embeddings.
method Using a parameterised surgery map to relate framed embeddings of S^1 to mapping class groups.
result Established connections between grasper families and known diffeomorphisms.
The unknot U in S^4 has non-unique smooth spanning 3-balls up to isotopy fixing U. Equivalently there are properly embedded non-separating 3-balls in S^1xB^3 not properly isotopic to 1xB^3. More generally there exist non-separating 3-spheres in S^1xS^3 not isotopic to 1xS^3 and non trivial elements of π_0 Diff_0(S^1xS^…
Infinite rank groups found in 3-manifolds with infinite fundamental groups.
problem Understanding the structure of diffeomorphism and homeomorphism groups of 3-manifolds with infinite fundamental groups.
method Analyzing actions of barbell diffeomorphisms on spaces of embedded arcs and configuration spaces.
result Groups of diffeomorphisms and homeomorphisms have infinite rank.
In the world of modern financial theory, portfolio construction has traditionally operated under at least one of two central assumptions: the constraints are derived from a utility function and/or the multivariate probability distribution of the underlying asset returns is fully known. In practice, both the performance…
Smooth manifolds have equivalent diffeomorphism groups if and only if they are diffeomorphic.
problem Understanding when diffeomorphism groups of smooth manifolds are elementarily equivalent.
method Analyzing the equivalence of Cr and Cs diffeomorphism groups of smooth manifolds. result Equivalent diffeomorphism groups imply diffeomorphic manifolds, strengthening previous results.
Constructs entropy-minimizing pseudo-Anosov diffeomorphisms on K3 surfaces.
problem Finding minimal entropy diffeomorphisms on K3 surfaces.
method Constructs pseudo-Anosov diffeomorphisms minimizing entropy.
result Obtains infinitely many entropy-minimizing diffeomorphisms.
The study proves diffeomorphisms can be localized to simpler submanifolds.
problem Localization of exotic diffeomorphisms on compact simply-connected 4-manifolds.
method Localization theorem for diffeomorphisms isotopic to identity after stabilization.
result Diffeomorphisms can be isotoped to simpler submanifolds.
Paper derives explicit expression of Alekseev-Meinrenken diffeomorphism.
problem Understanding the Alekseev-Meinrenken diffeomorphism.
method Via the Stokes phenomenon of meromorphic linear systems of ODEs with Poncaré rank 1.
result Explicit expression of the Alekseev-Meinrenken diffeomorphism.
According to Pixton, there are Morse-Smale diffeomorphisms of the 3-sphere which have no energy function, that is a Lyapunov function whose critical points are all periodic points of the diffeomorphism. We introduce the concept of quasi-energy function for a Morse-Smale diffeomorphism as a Lyapunov function with the le…
We determine the Riemannian manifolds for which the group of exact volume preserving diffeomorphisms is a totally geodesic subgroup of the group of volume preserving diffeomorphisms, considering right invariant L2-metrics. The same is done for the subgroup of Hamiltonian diffeomorphisms as a subgroup of the group of…
Study on group cocycles for volume-preserving diffeomorphisms.
problem Understanding group cocycles on volume-preserving diffeomorphisms.
method Constructed two types of group cocycles on the volume-preserving diffeomorphism group.
result One cocycle yields the Euler class of flat sphere bundles for the sphere.
Book introduces Hofer's metric on symplectic diffeomorphisms.
problem Understanding dynamics and growth in symplectic geometry.
method Introduces Hofer's metric and analyzes its properties.
result Provides insights into the structure of symplectic diffeomorphisms.
Study local diffeomorphisms of conformal circles in pseudo-Riemannian manifolds.
problem Understanding local diffeomorphisms of conformal circles.
method Variations of conformal circles and pseudo-Riemannian manifolds.
result Local diffeomorphisms of conformal circles are conformal local diffeomorphisms.
Survey on foliations and diffeomorphism groups.
problem Relationship between algebraic and homotopical properties.
method Survey and analysis of existing literature.
result Explains the connection between diffeomorphism groups and foliations.
New exotic 4D spaces found using knot slicing techniques.
problem Finding non-diffeomorphic exotic 4D spaces.
method Using RBG links to create slice knots with non-diffeomorphic complements.
result Distinguished new exotic 4D spaces using end Floer homology.
The paper proves n-transitivity for equivariant diffeomorphisms of manifolds.
problem Proving n-transitivity for equivariant diffeomorphisms. method Analyzing the group of equivariant diffeomorphisms on proper smooth G-manifolds. result The group of equivariant diffeomorphisms acts n-transitively on M. New 4-manifolds with exotic diffeomorphisms found.
problem Existence of exotic diffeomorphisms in 4-manifolds.
method Proves existence of infinitely many contractible 4-manifolds with exotic diffeomorphisms.
result Infinitely many contractible 4-manifolds with absolutely exotic diffeomorphisms.
Study exotic Dehn twists in 4-manifolds, producing first known exotic diffeomorphisms.
problem Detecting exotic diffeomorphisms in 4-manifolds.
method 2-parameter families Seiberg-Witten theory over RP2. result Constructed the smallest closed 4-manifold with exotic diffeomorphisms.
New Lie groups found for Poisson diffeomorphisms.
problem Finding Lie group structures on Poisson diffeomorphism groups.
method Using Poisson groupoids, develop Lie group structures.
result Poisson diffeomorphism groups of various Poisson manifolds are regular Lie groups.
An area-preserving diffeomorphism of an annulus has an "action function" which measures how the diffeomorphism distorts curves. The average value of the action function over the annulus is known as the Calabi invariant of the diffeomorphism, while the average value of the action function over a periodic orbit of the di…
Paper finds exotic diffeomorphisms on specific 4-manifolds.
problem Understanding exotic diffeomorphisms on 4-manifolds with b2+=2. method Comparing winding numbers of parameter families.
result 2\mathbb{C}\mathbb{P}^2 \# 10 (-\mathbb{C}\mathbb{P}^2) admits exotic diffeomorphisms.
Theta graph diffeomorphism shows nontrivial mapping class of 4-sphere.
problem Identifying nontrivial elements in the smooth mapping class group of 4-sphere.
method Diagrammatic calculus for smooth mapping class group of 4-sphere, Watanabe's clasper surgery construction.
result Theta graph diffeomorphism is isotopic to a nontrivial element of (1,2)-subgroup.
The paper finds diffeomorphic complex intersections with distinct Hodge numbers.
problem Identifying complex intersections with different Hodge numbers.
method Provided three pairs of 3-dimensional and one pair of 5-dimensional complex complete intersections, all diffeomorphic but with different Hodge numbers.
result Diffeomorphic complex intersections can have different Hodge numbers.
Positive paths connect diffeomorphisms on contact manifolds.
problem Defining and analyzing positivity in diffeomorphism groups of manifolds with contact structures.
method By examining paths of diffeomorphisms that are positively transverse to the contact distribution, showing flexibility and connecting diffeomorphisms.
result Any two diffeomorphisms on standard contact structure of R^(2n+1) can be connected by a positive path.
The paper proposes a deep learning approach to efficiently approximate diffeomorphisms for shape alignment.
problem Finding optimal reparameterizations of shapes for computing geodesic distances.
method The authors develop a neural network-based algorithm to construct approximations of diffeomorphisms using PyTorch.
result The proposed method achieves universal approximation properties and bounds on Lipschitz constants for the constructed diffeomorphisms.
Using the categorical description of supergeometry we give an explicit construction of the diffeomorphism supergroup of a compact finite-dimensional supermanifold. The construction provides the diffeomorphism supergroup with the structure of a Frechet supermanifold. In addition, we derive results about the structure of…
Proves transitivity of real Anosov diffeomorphisms with specific properties.
problem Transitivity of real Anosov diffeomorphisms with specific properties.
method Proves transitivity using specific properties of real Anosov diffeomorphisms.
result Proves transitivity of real Anosov diffeomorphisms.
We give examples of harmonic cellular maps between negatively curved manifolds which are not diffeomorphisms but are homotopic to diffeomorphisms.
Study controllability of diffeomorphisms of simple polytopes.
problem Controllability of diffeomorphisms of simple polytopes.
method Lie group structure and controllability results for diffeomorphisms of simple polytopes.
result Identity component of the diffeomorphism group is generated by the exponential image.
Diffeomorphisms of convex polytopes form a Lie group.
problem Understanding transformations of convex polytopes.
method Forming a Lie group from diffeomorphisms of convex polytopes.
result The group of diffeomorphisms of a convex polytope is a regular Lie group.
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…
Dual pairs constructed for volume preserving diffeomorphisms using symplectic geometry.
problem Understanding the group of volume preserving diffeomorphisms through symplectic geometry.
method Using cotangent bundles of spaces of smooth embeddings, symplectic reduction, and nonlinear Grassmannians of augmented submanifolds.
result Descriptions of coadjoint orbits of the group of volume preserving diffeomorphisms in terms of submanifolds of augmented spaces.
The π2-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 on the absolute value of sectional curvature and diameter of M. In this paper, w…
Authors prove existence of exotic surfaces and invariants not detecting self-diffeomorphisms.
problem Existence and properties of exotic surfaces and diffeomorphisms.
method Vanishing theorem of family Bauer--Furuta invariant for diffeomorphisms on spin 4-manifolds.
result Family Bauer--Furuta invariants do not detect exotic self-diffeomorphisms on S4 or S2imesS2. We prove that a compactly supported homeomorphism of a smooth manifold of dimension greater or equal to 5 can be approximated uniformly by compactly supported diffeomorphisms if and only if it is isotopic to a diffeomorphism. If the given homeomorphism is in addition volume preserving, then it can be approximated unifo…
Criteria for lifting manifold diffeomorphisms to vector bundle automorphisms.
problem Lifting diffeomorphisms to vector bundles.
method Criteria for lifting diffeomorphisms to linear automorphisms of vector bundles.
result Criteria for lifting diffeomorphisms to linear automorphisms of vector bundles.
Exotic diffeomorphisms found on complex surfaces and 4-manifolds.
problem Finding exotic diffeomorphisms on 4-manifolds.
method Minimal complex surfaces and spin 4-manifolds with S3 boundary. result First known instances of exotic diffeomorphisms of irreducible 4-manifolds.
Study partially hyperbolic diffeomorphisms in 3D, focusing on foliations and dynamics.
problem Classify 3D partially hyperbolic diffeomorphisms homotopic to the identity.
method Analyze Burago and Ivanov's branching foliations in Seifert fibered and hyperbolic manifolds.
result Complete classification of diffeomorphisms in Seifert fibered manifolds, and new potential class in hyperbolic manifolds.
The paper studies quasimorphisms on density-preserving diffeomorphisms of the Möbius band.
problem Exploring quasimorphisms on groups of diffeomorphisms of non-orientable manifolds.
method Investigates the group of density-preserving diffeomorphisms on the Möbius band and shows the existence of unbounded quasimorphisms.
result The group of density-preserving diffeomorphisms on the Möbius band admits countably many unbounded quasimorphisms.
The paper constructs a nontrivial diffeomorphism in 4-manifold topology.
problem Constructing a nontrivial diffeomorphism in 4-manifold topology.
method Using lens-shaped models and the second obstruction to pseudoisotopy.
result The constructed diffeomorphism is not isotopic to the identity.
We consider general Morse-Smale diffeomorphisms on a closed orientable two-dimentional surface. In this paper it is proved that the complete topological invariant of Morse-Smale diffeomorphisms is finite, the algorithm of the construction of the complete topological invariant in explicit form is given and necessary and…
We consider the following problem: given two parallel and identically oriented bundles of light rays in n-dimensional Euclidean space and given a diffeomorphism between the rays of the former bundle and the rays of the latter one, is it possible to realize this diffeomorphism by means of several mirror reflections? We …
No contact Anosov diffeomorphisms exist on odd-dimensional manifolds.
problem Existence of contact Anosov diffeomorphisms on odd-dimensional manifolds.
method Analysis of Anosov diffeomorphisms and invariant contact structures.
result No invariant contact structure exists for Anosov diffeomorphisms on odd-dimensional manifolds.
Extends Palais' result on diffeomorphisms to homeomorphisms and bi-Lipschitz mappings.
problem Extending diffeomorphisms to global mappings of manifolds.
method Elementary argument for diffeomorphisms, deep results for homeomorphisms and bi-Lipschitz mappings.
result Extension of Palais' result to homeomorphisms and bi-Lipschitz mappings.