arXiv research

Spectral sequence analysis for Sobolev mappings in Carnot groups.

Existence of an infinite sequence of harmonic maps between spheres of certain dimensions was proven by Bizon and Chmaj. This sequence shares many features of the Bartnik-McKinnon sequence of solutions to the Einstein-Yang-Mills equations as well as sequences of solutions that have arisen in other physical models. We ap…

We provide an explicit section for a mapping class group sequence.

The paper studies mapping class groups of 3-manifolds fibered over surfaces.

Paper presents new cobordism sequences for singular maps.

The curve graph and related graphs are hyperbolic and have quasi-tree fibers.

Study index bounds for harmonic maps sequences with bubbles.

Study connects Gaussian processes and regularization for sequence-function mappings.

We define two transforms between non-conformal harmonic maps from a surface into the 3-sphere. With these transforms one can construct, from one such harmonic map, a sequence of harmonic maps. We show that there is a correspondence between non-conformal harmonic maps into the 3-sphere, $H$-surfaces in Euclidean 3-space…

The paper studies splitting maps in link Floer homology using skein exact sequences.

In this paper we prove a compactness theorem for a sequence of harmonic maps which are defined on a converging sequence of Riemannian manifolds.

Study of orbifold mapping class groups via arc and curve actions.

We construct a closed Riemannian manifold $(N,h)$ and a sequence of $α$-harmonic maps from $S^2$ into $N$ with uniformly bounded energy such that the energy identity for this sequence is not true.

We establish a long exact sequence for Legendrian submanifolds L in P x R, where P is an exact symplectic manifold, which admit a Hamiltonian isotopy that displaces the projection of L off of itself. In this sequence, the singular homology H_* maps to linearized contact cohomology CH^* which maps to linearized contact …

Constructs Serre spectral sequence for bounded cohomology.

We show that the Korevaar-Schoen limit of the sequence of equivariant harmonic maps corresponding to a sequence of irreducible $SL_2({\mathbb C})$ representations of the fundamental group of a compact Riemannian manifold is an equivariant harmonic map to an ${\mathbb R}$-tree which is minimal and whose length function …

We introduce and study a new spectral sequence associated with a Poisson group action on a Poisson manifold and an equivariant momentum mapping. This spectral sequence is a Poisson analog of the Leray spectral sequence of a fibration. The spectral sequence converges to the Poisson cohomology of the manifold and has the…

Motivation. Protein contact map describes the pairwise spatial and functional relationship of residues in a protein and contains key information for protein 3D structure prediction. Although studied extensively, it remains very challenging to predict contact map using only sequence information. Most existing methods pr…

We show that for a strongly convergent sequence of purely loxodromic finitely generated Kleinian groups with incompressible ends, Cannon-Thurston maps, viewed as maps from a fixed base limit set to the Riemann sphere, converge uniformly. For algebraically convergent sequences we show that there exist examples where eve…

We define a generalization of Coxeter graphs and an associated Coxeter system and Coxeter mapping class. These can be used to construct periodic Coxeter mapping classes on surfaces with arbitrarily large genus, preserving lots of symmetries. The periodic mapping classes can in turn be used to construct sequences of pse…

Study continuity of limit sets in symmetric spaces.

We construct sequences of pseudo-Anosov mapping classes whose dilatations behave asymptotically like the inverse of the Euler characteristic of the surface they are defined on. These sequences are used to show that if the genus, g, and punctures, n, of a surface are related by a rational ray g=rn then the minimal dilat…

Defines cobordism maps connecting Khovanov and instanton homologies.

Attention is an operation that selects some largest element from some set, where the notion of largest is defined elsewhere. Applying this operation to sequence to sequence mapping results in significant improvements to the task at hand. In this paper we provide the mathematical definition of attention and examine its …

In this work, a novel sequential Monte Carlo filter is introduced which aims at efficient sampling of high-dimensional state spaces with a limited number of particles. Particles are pushed forward from the prior to the posterior density using a sequence of mappings that minimizes the Kullback-Leibler divergence between…

The definition of the grafting operation for quasifuchsian groups is extended by Bromberg to all $b$-groups. Although the grafting maps are not necessarily continuous at boundary groups, in this paper, we show that the grafting maps take every "standard" convergent sequence to a convergent sequence. As a consequence of…

In this paper, we study the blow-up phenomena on the $α_k$-harmonic map sequences with bounded uniformly $α_k$-energy, denoted by $\{u_{α_k}: α_k>1 \quad \mbox{and} \quad α_k\searrow 1\}$, from a compact Riemann surface into a compact Riemannian manifold. If the Ricci curvature of the target manifold is of a positive l…

This paper answers a basic question about the Birman exact sequence in the theory of mapping class groups. We prove that the Birman exact sequence does not admit a section over any subgroup $Γ$ contained in the Torelli group with finite index. A fortiori this proves that there is no section of the Birman exact sequence…

We study the Birman exact sequence for compact $3$--manifolds, obtaining a complete picture of the relationship between the mapping class group of the manifold and the mapping class group of the submanifold obtained by deleting an interior point. This covers both orientable manifolds and non-orientable ones.

Continuous time analysis of bubble formation in harmonic maps.

The paper develops a convex parameterization for robust RNNs ensuring stability and robustness.

This paper provides an infinite presentation for a subgroup of mapping class groups of non-orientable surfaces.

Study on harmonic maps from surfaces to homogeneous spaces, focusing on bubble formation and geometric constraints.

We analyze the signature type of a cascade of periodic orbits associated to period doubling renormalizable maps of the two dimensional disk. The signature is a sequence of rational numbers which describes how periodic orbits turn each other and is invariant by topological conjugacies that preserve orientation. We prove…

Introduces hierarchical uncertainty using U-sequences.

Strong stability of ergodic iterations proven without ergodic driving sequence.

Study on harmonic maps from surfaces with energy bounds and neck domains.

Polynomial representations found in surface braid and mapping class groups.

Study existence of harmonic and Dirac-harmonic maps from degenerating surfaces.

In this paper we prove the existence of a natural mapping from the surgery exact sequence for topological manifolds to the analytic surgery exact sequence of N. Higson and J. Roe. This generalizes the fundamental result of Higson and Roe, but in the treatment given by Piazza and Schick, from smooth manifolds to topolog…

We describe the Lorenz links generated by renormalizable Lorenz maps with reducible kneading invariant $(K_f^-,K_f^+)=(X,Y)*(S,W)$, in terms of the links corresponding to each factor. This gives one new kind of operation that permits us to generate new knots and links from old. Using this result we obtain explicit form…

Stability of Dehn functions proven for ultralimits of Sobolev maps.

In this paper we elaborate a general homotopy-theoretic framework in which to study problems of descent and completion and of their duals, codescent and cocompletion. Our approach to homotopic (co)descent and to derived (co)completion can be viewed as $\infty$-category-theoretic, as our framework is constructed in the …

We prove the energy identity and the no neck property for a sequence of smooth extrinsic polyharmonic maps with bounded total energy.

Many-to-Many VTN improves voice conversion across multiple speakers.

We construct a covering of Culler-Vogtmann Outer space by the Teichmuller spaces of punctured surfaces. By considering the equivariant homology for the action of Out(F_n) on this covering, we construct a spectral sequence converging to the homology of Out(F_n) that has E^1 terms given by the homology of mapping class g…

Study shows certain subgroups of fibered 3-manifolds are convex cocompact.

This paper presents a new exact sequence for orbifold braid groups and mapping class groups.