相关论文: On spectral decomposition of Smale-Vietoris axiom …
By studying braid group actions on Milnor's construction of the 1-sphere, we show that the general higher homotopy group of the 3-sphere is the fixed set of the pure braid group action on certain combinatorially described group. We also…
In this paper, we establish new normal scalar curvature inequalities on a class of austere submanifolds by proving sharper DDVV-type inequalities on associated austere subspaces. We also provide some examples of austere submanifolds in this…
In this paper, we give a uniqueness theorem for the Dirichlet problem of minimal maps into general Riemannian manifolds with non-positive sectional curvature, improving Theorem 5.2 of Lee-Ooi-Tsui's paper published in J. Geom. Anal.. The…
In earlier papers, we showed a decomposition of the arcs of 2-diregular digraphs (2-dds) and used it to prove some conditions for these graphs to be non-Hamiltonian; we then extended this decomposition to a larger class of digraphs and used…
We show the existence of a weak bi-invariant symmetric nondegenerate 2-form on the symplectic diffeomorphisms group $\mathcal{D}_\omega$ of a symplectic Riemannian manifold $(M,g,\omega)$ and study its properties. We describe the Euler's…
An SU(3)- or SU(1,2)-structure on a 6-dimensional manifold N^6 can be defined as a pair of a 2-form omega and a 3-form rho. We prove that any analytic SU(3)- or SU(1,2)-structure on N^6 with d omega^2 =0 can be extended to a parallel…
We establish an existence and uniqueness theorem for prime decompositions of theta-curves in $3$-manifolds.
This paper's theme is the relation between several classical and well-known objects: triangle Fuchsian groups, quasi-homogeneous singularities of plane curves, torus knot complements in the 3-sphere. Torus knots are the only nontrivial…
In the present work, we study the decompositions of codimension-one transitions that alter the singular set the of stable maps of $S^3$ into $\mathbb{R}^3,$ the topological behaviour of the singular set and the singularities in the branch…
We define cusp-decomposable manifolds and prove smooth rigidity within this class of manifolds. These manifolds generally do not admit a nonpositively curved metric but can be decomposed into pieces that are diffeomorphic to finite volume,…
It is conjectured that every manifold admitting an Anosov diffeomorphism is, up to homeomorphism, finitely covered by a nilmanifold. Motivated by this conjecture, an important problem is to determine which nilmanifolds admit an Anosov…
A smooth diffeomorphism is said to be distributionally uniquely ergodic (DUE for short) when it is uniquely ergodic and its unique invariant probability measure is the only invariant distribution (up to multiplication by a constant).…
An affine manifold is a manifold with an affine structure, i.e. a torsion-free flat affine connection. We show that the universal cover of a closed affine 3-manifold $M$ with holonomy group of shrinkable dimension (or discompacit\'e in…
We investigate Atiyah algebroids, i.e. the infinitesimal objects of principal bundles, from the viewpoint of Lie algebraic approach to space. First we show that if the Lie algebras of smooth sections of two Atiyah algebroids are isomorphic,…
We prove that there exist diffeomorphisms of tori, supported in a disc, which are not isotopic to symplectomorphisms with respect to any symplectic structure. This yields a partial negative answer to a question of Benson and Gordon about…
We prove that any diffeomorphism of a compact manifold can be C^1-approximated by a diffeomorphism which exhibits a homoclinic bifurcation (a homoclinic tangency or a heterodimensional cycle) or by a diffeomorphism which is partially…
We construct Anosov diffeomorphisms on manifolds that are homeomorphic to infranilmanifolds yet have exotic smooth structures. These manifolds are obtained from standard infranilmanifolds by connected summing with certain exotic spheres.…
We study invariants associated to Smale spaces obtained from an expanding endomorphism on a (closed connected Riemannian) flat manifold. Specifically, the relevant invariants are the $K$-theory of the associated $C^*$-algebras and Putnam's…
We prove the existence of non-trivial irreducible SU(2)-monopoles with Dirac singularities on any rational homology 3-sphere, equipped with any Riemannian metric, using a gluing construction.
We formulate a very general conjecture relating the analytical invariants of a normal surface singularity to the Seiberg-Witten invariants of its link provided that the link is a rational homology sphere. As supporting evidence, we…