Study on large scale surjections and their properties.
problem Properties of large scale surjections and their invariants.
method Coarse disjointness and large scale n-to-1 functions.
result Characterization of asymptotic dimension for coarse structures.
The paper examines the co-rank of weakly parafree 3-manifold groups and provides counterexamples.
problem Investigating the co-rank of weakly parafree 3-manifold groups and their relationship to free groups.
method Constructing specific examples of homology handlebodies and analyzing their fundamental groups.
result The fundamental group of W. Thurston's tripus manifold is not very large, showing that weakly parafree groups of rank at least 3 are not necessarily very large.
The symplectic representation of mapping classes is not surjective for certain types of mapping classes.
problem The surjectivity of the symplectic representation of mapping classes, particularly pseudo-Anosov ones, is not always preserved.
method Explicit construction of symplectic matrices with a bi-Perron leading eigenvalue that cannot be represented by orientable pseudo-Anosov mapping classes.
result The symplectic representation of orientable pseudo-Anosov mapping classes is not surjective.
The paper proves neural networks are almost always surjective, impacting model safety.
problem Ensuring neural networks can generate any output, including harmful content.
method Analyzing fundamental neural architectures and generative models.
result Many neural architectures are almost always surjective, allowing for arbitrary outputs.
The paper introduces two-tone colorings for links and shows conditions for surjective dihedral representations.
problem The challenge is to find conditions for links to admit surjective dihedral representations.
method The method involves introducing two-tone colorings and providing conditions for the link groups to admit such representations.
result Any link with at least 3 components admits a surjective homomorphism to the dihedral group of arbitrary degree.
The aim of this paper (inspired from a problem of Habegger) is to describe the set of cubical decompositions of compact manifolds mod out by a set of combinatorial moves analogous to the bistellar moves considered by Pachner, which we call bubble moves. One constructs a surjection from this set onto the the bordism gro…
Simplified proof of K3 surface period map surjectivity.
problem Surjectivity of period map on K3 surfaces.
method Utilizes hyperkähler geometry and collapsing techniques.
result Simple proof of Todorov's result on K3 surfaces.
The Hilbert map's image is discussed, showing when it's surjective.
problem Understanding when the Hilbert map is surjective.
method Analyzing the Hilbert map's properties to determine surjectivity.
result Necessary and sufficient conditions for the Hilbert map to be surjective.
If phi: G-->G' is a surjective homomorphism, we prove that the twisted Alexander polynomial of G is divisible by the twisted Alexander polynomial of G'. As an application, we show non-existence of surjective homomorphism between certain knot groups.
Proves generic surjectivity of vector bundles via degeneration.
problem Understanding generic surjectivity of vector bundles.
method Uses degeneration argument, Berndtsson's theorem, and Lempert's proof.
result Generalizes previous work on L2 division theorem. Proves surjectivity of certain smooth maps with non-properness sets.
problem Surjectivity of linear operators and global diffeomorphisms of semialgebraic maps.
method Analytic proof involving C∞ semialgebraic local diffeomorphisms and linear partial differential operators. result A new analytic conjecture for polynomial local diffeomorphisms of Rn implies known results. Kirwan surjectivity proved for K-contact manifolds with free S^1-action.
problem Proving Kirwan surjectivity for K-contact manifolds.
method Analogue of Kirwan surjectivity in equivariant basic cohomology.
result Symplectic manifold quotient reproduces Kirwan's surjectivity.
A map's critical points and surjectivity are linked in this note.
problem Understanding the critical points and surjectivity of smooth maps between manifolds.
method Analyzing the critical points and dimension of their collection for smooth maps between manifolds.
result The dimension of the critical points collection is at least n-1, affecting surjectivity.
Period maps surjective for certain gravitational instantons.
problem Understanding the uniformization of gravitational instantons.
method Uniformization theorems by Chen--Chen, Chen--Viaclovsky, Collins--Jacob--Lin, and Hein--Sun--Viaclovsky--Zhang.
result Period maps surjective for ALH*, ALG, and ALG* gravitational instantons.
VAEs struggle with surjective multimodal data, especially class labels describing images.
problem VAEs struggle to capture variability in surjective multimodal data.
method Theoretical and empirical demonstration of VAEs with a mixture of experts posterior.
result VAEs with a mixture of experts posterior can disregard variation in surjective multimodal data.
The paper studies symmetries in quandles and their relative versions.
problem Understanding symmetries in quandle structures and their transformations.
method Introducing relative versions of inner automorphism and transvection groups, and using them to characterize and classify surjective homomorphisms.
result Characterization of connected homomorphisms and classification of quandle structures under certain symmetry assumptions.
Eisenhart's theorem extended to sub-Riemannian metrics on specific Lie algebras.
problem Extending Eisenhart's theorem to sub-Riemannian metrics on step 2 distributions.
method Introducing ad-surjective step 2 nilpotent Lie algebras and extending Eisenhart's theorem.
result The theorem holds for sub-Riemannian metrics on ad-surjective step 2 distributions.
Study surjectivity of Kirwan map for generalized hyperkähler reduction.
problem Establishing surjectivity of Kirwan map for a specific class of Hamiltonian manifolds.
method Defined a close analogue of hyperkähler reduction for manifolds with equivariant functions under semi-linear G-actions. result Surjectivity of Kirwan map proved for the defined class of manifolds.
Let G be a compact Lie group, and let LG denote the corresponding loop group. Let (X,ω) be a weakly symplectic Banach manifold. Consider a Hamiltonian action of LG on (X,ω), and assume that the moment map $μ: X \to L\fg^*$ is proper. We consider the function ∣μ∣2:X→R, and use a version of Morse theor…
We prove that if Y is the Gromov-Hausdorff limit of a sequence of compact manifolds, Min, with a uniform lower bound on Ricci curvature and a uniform upper bound on diameter, then Y has a universal cover. We then show that, for i sufficiently large, the fundamental group of Mi has a surjective homeomorphis…
A group is known as `large' if some finite index subgroup admits a surjective homomorphism onto a non-abelian free group. In this paper, we give a necessary and sufficient condition for a finitely presented group to be large, in terms of the existence of a normal series where successive quotients are finite abelian gro…
Study surjections between braid groups on surfaces, focusing on lower central series.
problem Determine conditions for surjections between braid groups on surfaces.
method Utilizes properties of lower central series and combinatorial methods.
result Identifies specific values of m and n for which surjections exist between braid groups.
This paper is motivated by a relatively recent work by Joyce in special Lagrangian geometry, but the basic idea of the present paper goes back to an earlier pioneering work of Donaldson in Yang--Mills gauge theory; Donaldson discovered a global structure of a (compactified) moduli space of Yang--Mills instantons, and a…
We prove that while there are maps $\bT^4\to\#^3(\bS^2\times\bS^2)$ of arbitrarily large degree, there is no branched cover from 4-torus to $\#^3(\bS^2\times \bS^2)$. More generally, we obtain that, as long as N satisfies a suitable cohomological condition, any π1-surjective branched cover $\bT^n \to N$ is a hom…
The paper proves that certain surface mapping class groups do not virtually surject to the integers.
problem Proving that certain mapping class groups do not virtually surject to the integers.
method Analyzing the structure of finite-index subgroups of mapping class groups of surfaces of genus ≥ 3.
result Finite-index subgroups of mapping class groups of surfaces of genus ≥ 3 do not virtually surject to the integers.
We use Klyachko's methods to prove that the natural map G to G-hat, where G is a torsion-free group and G-hat is obtained by adding a new generator t and a new relator w, is surjective only if w is conjugate to gt or gt^{-1} for some g in G. This solves a special case of the surjectivity problem for group extensions, r…
For any closed Riemannian manifold X we prove that large isoperimetric regions in X×Rn are of the form X×(Euclidean ball). We prove that if X has non-negative Ricci curvature then the only soap bubbles enclosing a large volume are the products X×(Euclidean sphere). We give an example…
Kirwan surjectivity proven for equivariant Dolbeault cohomology.
problem Understanding cohomology of Kähler quotients for Hamiltonian actions.
method Using Cartan-Chern-Weil theory to define and prove a Kirwan map.
result A natural surjective Kirwan map established between equivariant Dolbeault cohomologies.
Study differential invariants of objects and their images under surjective maps.
problem Reconstruction of objects from multiple-view images.
method Analysis of differential invariants under surjective maps, considering projectable and non-projectable cases.
result Constructible isomorphism between object and image invariants in the projectable case.
Surjectivity of Cannon-Thurston map proven for metric graph bundles.
problem Proving surjectivity of Cannon-Thurston map in metric graph bundles.
method Generalized Mj-Sardar's result to include more types of fibers.
result Continuous extension map between boundaries is surjective.
A group is known as `large' if some finite index subgroup admits a surjective homomorphism onto a non-abelian free group. The main theorem of the paper is as follows. Let G be a finitely generated, large group and let g_1,...,g_r be a collection of elements of G. Then G/<<g_1^n,...,g_r^n>> is also large, for infinitely…
The paper shows how surjective homomorphisms between surface braid groups factor and computes their automorphism groups.
problem Characterizing surjective homomorphisms and automorphisms of surface braid groups.
method Analyzing the structure of surface braid groups and their homomorphisms.
result Surjective homomorphisms factor through forgetful maps and automorphisms are geometric.
P. Buser and P. Sarnak showed in 1994 that the maximum, over the moduli space of Riemann surfaces of genus s, of the least conformal length of a nonseparating loop, is logarithmic in s. We present an application of (polynomially) dense Euclidean packings, to estimates for an analogous 2-dimensional conformal systolic i…
This paper extends Thurston and Tsuboi's work on foliations of S3.
problem Proving surjectivity and splitting of homomorphisms related to foliations.
method Real analytic construction and modification of Thurston and Tsuboi's arguments.
result Proves the splitting of the second homomorphism and lifts Tsuboi's subgroup.
Let K be a prime knot in S3 and G(K)=π1(S3−K) the knot group. We write K1≥K2 if there exists a surjective homomorphism from G(K1) onto G(K2). In this paper, we determine this partial order on the set of prime knots with up to 11 crossings. There exist such 801 prime knots and then 640,800 shou…
This paper uses Morse-theoretic techniques to compute the equivariant Betti numbers of the space of semistable rank two degree zero Higgs bundles over a compact Riemann surface, a method in the spirit of Atiyah and Bott's original approach for semistable holomorphic bundles. This leads to a natural proof that the hyper…
Let G be a compact connected Lie group, and (M,ω) a Hamiltonian G-space with proper moment map μ. We give a surjectivity result which expresses the K-theory of the symplectic quotient M//G in terms of the equivariant K-theory of the original manifold M, under certain technical conditions on μ. This result is a natural …
We study completeness properties of the Sobolev diffeomorphism groups Ds(M) endowed with strong right-invariant Riemannian metrics when the underlying manifold M is Rd or compact without boundary. The main result is that for s>dimM/2+1, the group Ds(M) is geodesically and me…
Maps between classifying spaces for certain groups are studied, with rational cohomology results.
problem Analyzing maps between classifying spaces for specific groups.
method Study of maps Θ between null-components of homomorphism and based map spaces. result Surjectivity of map Θ in rational cohomology for certain groups, and non-surjectivity for others. Finite-gap solutions approximate jets of initial data for certain BKM systems.
problem Approximating jets of initial data for specific PDE systems.
method Using finite-reduction map to finite-gap solutions of Stäckel systems.
result Full jet-surjectivity for KdV and Kaup--Boussinesq, partial for Camassa--Holm.
Modified constraint operator for localized deformation with dominant energy condition.
problem Handling localized deformation with initial data sets under the dominant energy condition.
method Introduced a modified constraint operator to absorb metric changes and established local surjectivity theorem.
result Promoted dominant energy condition to strict inequality through compactly supported variations.
This paper proves a map from flow-spines to contact structures is surjective.
problem Mapping flow-spines to contact structures in 3-manifolds.
method Using positive flow-spines and contact structures, proving surjectivity.
result The map from flow-spines to contact structures is surjective.
SSNL improves simulation-based inference for high-dimensional data.
problem Performance degradation in neural likelihood estimation for high-dimensional data.
method Surjective Sequential Neural Likelihood (SSNL) using surjective normalizing flow models.
result SSNL avoids manual crafting of summary statistics and outperforms state-of-the-art methods.
Injective and surjective neural operators for function spaces.
problem Tackles injective and surjective neural operators in function spaces.
method Combines prior work in ReLU and operator learning, uses Fredholm theory and Leray-Schauder degree theory.
result Injective and surjective neural operators are universal approximators and maintain their properties in finite-rank implementations.
Continuous map from circle to sphere determined by surface bundle triangulation.
problem Understanding the order of filling a sphere by a continuous map from a circle.
method Introduced triangulation of surface bundles by Agol; uses invariant foliations.
result Order of filling sphere is dictated by natural triangulation of surface bundle.
Study of homology commutativity in separable metrizable spaces.
problem Homology commutativity in separable metrizable spaces.
method Computations and analysis of homology approximants and maps.
result Affirmative solution to the surjectivity problem for locally compact spaces in cohomology.
New properties established for SO(3) quantum representations, showing density and surjectivity.
problem Properties of SO(3) quantum representations of mapping class groups.
method Analyzing roots of unity and maximal ideals of Z[ζ_p] to establish properties.
result SO(3) quantum representations have dense image and are surjective modulo unramified maximal ideals.
New rigidity theorem on static manifolds with boundary.
problem Static metrics on manifolds with boundary.
method Obata-type rigidity theorem, sufficient geometric conditions.
result Scalar curvature map can be locally surjective at static metrics on manifolds with boundary.