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.
Exotic diffeomorphism survives stabilizations on a contractible 4-manifold.
problem Finding exotic diffeomorphisms on contractible 4-manifolds.
method Developed a Pin(2) × Z_2-equivariant refinement for computing Seiberg-Witten Floer homotopy types.
result Constructed an exotic diffeomorphism that survives two stabilizations.
New method distinguishes 4-manifold types using trisections.
problem Distinguishing different 4-manifold types.
method Capping operation to transform relative trisections into closed 4-manifold diagrams.
result Examples of non-diffeomorphic relative trisections of the same 4-manifold.
Classifies 3D spaces using specific invariants.
problem Classifying 3D simply connected Mori fibre spaces.
method Uses finitely many numerical invariants.
result Finds finitely many invariants to classify diffeomorphism types.
Researchers calculate the cohomology of a specific lens space combination.
problem Calculating the cohomology of a specific lens space combination.
method Using the homotopy type of generic lens spaces and a theorem by Hatcher.
result The cohomology ring of the diffeomorphism group of the lens space combination.
Study shows diffeomorphism groups of certain 3-manifolds retract to isometry groups.
problem Understanding the structure of diffeomorphism groups of 3-manifolds.
method Deformation retraction and earlier work by multiple authors combined.
result Homotopy type of Diff(X) determined for prime 3-manifolds.
Researchers simplify the computation of diffeomorphism groups for Morse-Bott foliations.
problem Computing the homotopy type of diffeomorphism groups for Morse-Bott foliations.
method Reduces the computation to three groups: diffeomorphisms of the critical manifold, vector bundle automorphisms, and fixed near the critical manifold.
result Shows how to compute the homotopy type of diffeomorphism groups for certain Morse-Bott foliations.
Knot lattice homology invariant is preserved under certain 3-manifold diffeomorphisms.
problem Preserving knot lattice homology invariants under 3-manifold diffeomorphisms.
method Examined filtered lattice chain homotopy types of negative-definite forests with one unframed vertex.
result Filtered lattice chain homotopy type is an invariant of the diffeomorphism type of resulting 3-manifolds.
We show that a Laplace isospectral family of two dimensional Riemannian orbifolds, sharing a lower bound on sectional curvature, contains orbifolds of only a finite number of orbifold category diffeomorphism types. We also show that orbifolds of only finitely many orbifold diffeomorphism types may arise in any collecti…
Real Lagrangians in toric manifolds are classified by combinatorial data.
problem Classifying real Lagrangian submanifolds in toric symplectic manifolds.
method Established a real analog of the Delzant construction.
result Real Lagrangians in toric del Pezzo surfaces have all possible diffeomorphism types.
Unique symplectic fillings found for specific cotangent bundles.
problem Symplectic fillings of unit cotangent bundles.
method Proved uniqueness up to diffeomorphism.
result Unique symplectically aspherical fillings found.
In this note we prove that equivariantly homeomorphic quasitoric manifolds are diffeomorphic. As a consequence we show that up to finite ambiguity the diffeomorphism type of certain quasitoric manifolds M is determined by their cohomology rings and first Pontrjagin classes.
The paper proves a finite diffeomorphism theorem for manifolds with lower Ricci curvature and bounded energy.
problem Proving a finite number of diffeomorphism types for manifolds with specific curvature and energy bounds.
method Analyzing the space of closed manifolds with lower Ricci curvature, volume, diameter, and energy bounds.
result The space of manifolds has at most a finite number of diffeomorphism types.
In this paper we give a full diffeomorphism characterization of compact simply connected cohomogeneity one manifolds in dimension six.
ALE Kähler surfaces have finitely many types.
problem Classifying ALE Kähler surfaces.
method Resolution of quotient singularities and deformation theory.
result Only finitely many diffeomorphism types exist.
Generalizes π2-diffeomorphism finiteness to non-zero first homotopy groups.
problem Bounding diffeomorphic types of compact manifolds with vanishing first and second homotopy groups.
method Generalizing the π2-diffeomorphism finiteness theorem to include non-zero first homotopy groups. result Diffeomorphic types of compact manifolds with non-zero first homotopy groups can be bounded.
In this paper we investigate the relationship between isotopy classes of knots and links in S^3 and the diffeomorphism types of homeomorphic smooth 4-manifolds. As a corollary of this initial investigation, we begin to uncover the surprisingly rich structure of diffeomorphism types of manifolds homeomorphic to the K3 s…
The Gluck twist preserves the diffeomorphism type of certain satellite 2-knots.
problem Preserving the diffeomorphism type of satellite 2-knots under the Gluck twist.
method Using new descriptions of satellite 2-knots, the paper shows that the Gluck twist does not change the diffeomorphism type of certain satellite 2-knots in three ways.
result The Gluck twist preserves the diffeomorphism type of certain satellite 2-knots.
Study on minimal submanifolds with finite curvature in Euclidean space.
problem Finite diffeomorphism types of complete immersed minimal submanifolds with finite total curvature.
method Adapted method from Chodosh, Ketover, and Maximo for hypersurfaces to submanifolds of arbitrary codimension.
result Proved finite diffeomorphism types for complete immersed minimal submanifolds with finite total curvature.
Surface corks modify 4-manifold structures without changing their homeomorphism type.
problem Understanding how to change 4-manifold structures using surface corks.
method Introducing surface corks as compact, contractible submanifolds intersecting smoothly embedded surfaces in 4-manifolds.
result Explicit construction of a transverse surface cork that is diffeomorphic to a 4-ball.
R-circles in general three dimensional CR manifolds (of contact type) are the analogues to traces of Lagrangian totally geodesic planes on the sphere viewed as the boundary of two dimensional complex hyperbolic space. They form a family of certain legendrian curves on the manifold. We prove that a diffeomorphism betwee…
Finite types of 4D manifolds with specific curvature, volume, and diameter.
problem Classifying 4D manifolds with given curvature, volume, and diameter constraints.
method Proving finiteness of diffeomorphism types for 4-manifolds with specified conditions.
result There are only finitely many diffeomorphism types of 4D manifolds with given curvature, volume, and diameter constraints.
Suppose M is a noncompact connected smooth 2-manifold without boundary and let D(M)_0 denote the identity component of the diffeomorphism group of M with the compact-open C^infty-topology. In this paper we investigate the topological type of D(M)_0 and show that D(M)_0 is a topological ell_2-manifold and it has the hom…
Two non-diffeomorphic minimal genus trisections found for a 4-manifold.
problem Existence of non-diffeomorphic minimal genus trisections of the same 4-manifold.
method Introduced a simple operation to create a trisection diagram from a relative trisection diagram.
result Existence of two non-diffeomorphic minimal genus trisections of the same (g,k;p,b)-type 4-manifold. Contractible diffeomorphism groups on lens spaces derived from Morse-Bott foliations.
problem Understanding the structure of diffeomorphism groups on lens spaces.
method Analyzing Morse-Bott foliations and their diffeomorphisms.
result Contractible diffeomorphism groups on lens spaces.
We prove a homological version of a conjecture about the homotopy type of diffeomorphism spaces of reducible 3-manifolds.
problem Proving a conjecture about the homotopy type of diffeomorphism spaces of reducible 3-manifolds.
method Homological approach to show finitely many nonzero homology groups, each finitely generated.
result BDiff(M, rel ∂) has finitely many nonzero homology groups, each finitely generated, for connected sums of irreducible 3-manifolds with nontrivial and non-spherical boundaries.
Study Stein fillings of planar contact 3-manifolds with relative trisection genus 2.
problem Classify Stein fillings of planar contact 3-manifolds under constraints on their relative trisections.
method Partial classification of diffeomorphism types of fillings with relative trisections of genus at most 2.
result Partially classify the diffeomorphism types of Stein fillings with relative trisections of genus at most 2.
Study decomposes geometric surfaces, finding special curves.
problem Existence of certain affine diffeomorphisms on translation surfaces.
method Explicit cylinder decomposition on geometric surfaces.
result Special curves are obstructions to certain diffeomorphisms.
We bring together those systems of hydrodynamical type that can be written as geodesic equations on diffeomorphism groups or on extensions of diffeomorphism groups with right invariant L2 or H1 metrics. We present their formal derivation starting from Euler's equation, the first order equation satisfied by the ri…
The paper connects diffeomorphism groups and sphere embeddings, proving a group structure.
problem Understanding the homotopy types of diffeomorphism groups and sphere embeddings.
method Cerf's upgraded proof, scanning maps, canceling handles, Embedding Calculus.
result The monoid of Schoenflies spheres forms a group under connect-sum.
Chernov-Nemirovski observed that the existence of a globally hyperbolic Lorentzian metric on a (3 + 1)-spacetime pins down a smooth structure on the underlying 4-manifold. In this paper, we point out that the diffeomorphism type of a globally hyperbolic (n + 1)-spacetime is determined by the h-cobordism class of its Ca…
Study of diffeomorphisms groups on lens spaces with Morse-Bott foliations.
problem Computing homotopy types of diffeomorphism groups of specific foliations.
method Analysis of leaf-preserving and foliated diffeomorphisms on lens spaces.
result Inclusion of leaf-preserving groups into foliated groups is a homotopy equivalence.
The Price twist creates three 4-manifolds from a 4-sphere.
problem Understanding the properties of a non-simply connected 4-manifold created from a 4-sphere.
method Cutting and pasting operation on a P2-knot S in a 4-manifold. result The non-simply connected 4-manifold τS(S4) is studied for Kinoshita type P2-knots. Study calculates homotopy groups and derivatives for disc diffeomorphisms.
problem Understanding the homotopy groups of diffeomorphisms of discs.
method Computes rational homotopy groups and uses Weiss' orthogonal calculus.
result Determines optimal rational concordance stable range for high-dimensional discs.
We compute the Eells-Kuiper invariant of the Berger manifold SO(5)/SO(3) and determine that it is diffeomorphic to the total space of an S^3-bundle over S^4. This answers a question raised by K. Grove and W. Ziller.
In this paper we prove that no complex surface of general type is diffeomorphic to a rational surface, thereby completing the smooth classification of rational surfaces and the proof of the Van de Ven conjecture on the smooth invariance of Kodaira dimension.
Extended surgery theory proves diffeomorphism for simply-connected 4k-manifolds.
problem Proving diffeomorphism for simply-connected 4k-manifolds.
method Construction of an extended surgery obstruction associated to a normal bordism.
result Identifies the inertia group of a (2k-1)-connected 4k-manifold.
We show that the group ${\Cal D}(M)$ of pseudoisotopy classes of diffeomorphisms of a manifold of dimension ≥5 and of finite fundamental group is commensurable to an arithmetic group. As a result π0(DiffM) is a group of finite type.
Unique symplectic fillings of odd spheres' cotangent bundles proven.
problem Uniqueness of symplectic fillings for odd-dimensional spheres' cotangent bundles.
method Proof of uniqueness up to diffeomorphism.
result Unique symplectically aspherical fillings of odd spheres' cotangent bundles.
This note deals with arbitrary Morse-Smale diffeomorphisms in dimension 3 and extends ideas from \cite{GrLaPo}, \cite{GrLaPo1}, where gradient-like case was considered. We introduce a kind of Morse-Lyapunov function, called dynamically ordered, which fits well dynamics of diffeomorphism. The paper is devoted to finding…
We construct Bott-type and stable equivariant Seiberg-Witten Floer homology and cohomology for rational homology spheres, and prove their diffeomorphism invariance.
The paper is devoted to finding conditions to the existence of a self-indexing energy function for Morse-Smale diffeomorphisms on a 3-manifold. These conditions involve how the stable and unstable manifolds of saddle points are embedded in the ambient manifold. We also show that the existence of a self-indexing energy …
We study global gravitational anomalies in type IIB string theory with nontrivial middle cohomology. This requires the study of the action of diffeomorphisms on this group. Several results and constructions, including some recent vanishing results via elliptic genera, make it possible to consider this problem. Along th…
Study constraints on diffeomorphisms and homeomorphisms of 4-manifolds with boundary.
problem Constraints on smooth families of 4-manifolds with boundary.
method Use Manolescu's Seiberg-Witten Floer stable homotopy type.
result Inclusion map between diffeomorphisms and homeomorphisms is not a weak homotopy equivalence.
A new type of diffeomorphic normalizing flow for flexible density estimation.
problem Flexible density estimation and variational inference.
method Constructs a diffeomorphic flow using an ODE with a neural network to parametrize the smooth vector field and a recursive neural network for approximating the solution.
result End-to-end trained DDNF achieves competitive results on density estimation and variational inference tasks.
New λ-hypersurfaces not isometric to standard spheres.
problem No Alexandrov theorem for λ-hypersurfaces. method Constructing compact embedded λ-hypersurfaces diffeomorphic to a sphere. result Found λ-hypersurfaces not isometric to standard spheres. We prove a Livsic type theorem for cocycles taking values in groups of diffeomorphisms of low-dimensional manifolds. The results hold without any localization assumption and in very low regularity. We also obtain a general result (in any dimension) which gives necessary and sufficient conditions to be a coboundary.
Researchers find multiple supporting minimal Lefschetz pencils for a complex fibration.
problem Finding multiple supporting minimal Lefschetz pencils for a specific Lefschetz fibration.
method Analyzing maximal disjoint (−1)-sections of the Matsumoto-Cadavid-Korkmaz Lefschetz fibration. result The Matsumoto-Cadavid-Korkmaz Lefschetz fibration has more than one supporting minimal Lefschetz pencils.