相关论文: The Pontrjagin-Hopf invariants for Sobolev maps

We study geometric variational problems for a class of effective models in quantum field theory known as Faddeev-Skyrme models. Mathematically one considers minimizing an energy functional on homotopy classes of maps from closed 3-manifolds…

In this paper we consider a generalization of the Faddeev model for the maps from a closed three-manifold into the two-sphere. We give a novel representation of smooth $ S^2$-valued maps based on flat connections. This representation allows…

Pseudo horizontally weakly conformal maps extend both holomorphic and (semi)conformal maps into an almost Hermitian manifold. We find in this larger class critical points for the (generalized) Faddeev-Hopf energy. Their stability is also…

We give an alternative to Postnikov's homotopy classification of maps from 3-dimensional CW-complexes to homogeneous spaces G/H of Lie groups. It describes homotopy classes in terms of lifts to the group G and is suitable for extending the…

We construct and discuss new numerical homotopy invariants of topological spaces that are suitable for the study of functions on loop and sphere spaces. These invariants resemble the Lusternik-Schnirelmann category and provide lower bounds…

Sobolev spaces are a natural framework for the analysis of problems in partial differential equations and calculus of variations. Some physical and geometric contexts, such as liquid crystals models and harmonic maps, lead to consider…

We study the invariant distributions for the horocycle map on $\Gamma\backslash SL(2, \mathbb{R})$ and prove Sobolev estimates for the cohomological equation of the horocycle map. As an application, we obtain an estimate for the rate of…

This manuscript develops a framework for the strong approximation of Sobolev maps with values in compact manifolds, emphasizing the interplay between local and global topological properties. Building on topological concepts adapted to VMO…

An approximation theorem of Youngs (1948) asserts that a continuous map between compact oriented topological 2-manifolds (surfaces) is monotone if and only if it is a uniform limit of homeomorphisms. Analogous approximation of Sobolev…

This paper presents and explores a theory of \emph{multiholomorphic maps}. This group of ideas generalizes the theory of pseudoholomorphic curves in a direction suggested by consideration of the kinds of compatible geometric structures that…

We generalize the notion of calibrated submanifolds to smooth maps and show that the several examples of smooth maps appearing in the differential geometry become the examples of our situation. Moreover, we apply these notion to give the…

A theory of finite type invariants for arbitrary compact oriented 3-manifolds is proposed, and illustrated through many examples arising from both classical and quantum topology. The theory is seen to be highly non-trivial even for…

In this paper we develop the theory of finite-type invariants for homologically nontrivial 3-manifolds. We construct an infinite-dimensional affine space with a hypersurface in it corresponding to manifolds with Morse singularities.…

This expository article discusses some connections between the geometry of a hyperbolic 3-manifold homotopy-equivalent to a surface, and the combinatorial properties of its end invariants. In particular a necessary and sufficient condition…

In [LMO] a 3-manifold invariant $\Omega(M)$ is constructed using a modification of the Kontsevich integral and the Kirby calculus. The invariant $\Omega$ takes values in a graded Hopf algebra of Feynman 3-valent graphs. Here we show that…

This paper studies invariants of 3-manifolds derived from certain fin ite dimensional Hopf algebras. The invariants are based on right integrals for these algebras. It is shown that the resulting class of invariants is distinct from the…

We show that the set of harmonic maps from the 2-dimensional stratified spheres with uniformly bounded energies contains only finitely many homotopy classes. We apply this result to construct infinitely many harmonic map flows and mean…

We obtain a compact Sobolev embedding for $H$-invariant functions in compact metric-measure spaces, where $H$ is a subgroup of the measure preserving bijections. In Riemannian manifolds, $H$ is a subgroup of the volume preserving…

This is a survey paper of author's results on cobordism groups and semigroups of fold maps and simple fold maps. The results include: establishing a relation between fold maps and immersions through geometrical invariants of cobordism…

As a higher dimensional version of the theory of Morse functions, there have been various studies of smooth manifolds using generic smooth maps. As fundamental results, in these studies, they have found that inverse images of such maps…