arXiv research

Complete classification of symmetric spaces actions.

Classifies symplectic torus actions up to equivariant symplectomorphism.

Classifies 4D Alexandrov spaces with torus actions.

The paper classifies actions of homeomorphism groups on manifolds.

The paper classifies actions on unit spheres and symmetric spaces.

We examine free orientation-reversing group actions on orientable handlebodies, and free actions on nonorientable handlebodies. A classification theorem is obtained, giving the equivalence classes and weak equivalence classes of free actions in terms of algebraic invariants that involve Nielsen equivalence. This is app…

We introduce the notion of a local torus action modeled on the standard representation (for simplicity, we call it a local torus action). It is a generalization of a locally standard torus action and also an underlying structure of a locally toric Lagrangian fibration. For a local torus action, we define two invariants…

New structural result classifies actions on symmetric spaces.

Study describes orbits of PSL(2, R) action on 3D Einstein universe.

Study cyclic group actions on specific high-dimensional manifolds.

Poisson actions of Poisson Lie groups have an interesting and rich geometric structure. We will generalize some of this structure to Dirac actions of Dirac Lie groups. Among other things, we extend a result of Jiang-Hua-Lu, which states that the cotangent Lie algebroid and the action algebroid for a Poisson action form…

Let G be a connected semisimple Lie group without compact factors whose real rank is at least 2, and let Γ\subset G be an irreducible lattice. We provide a C^\infty classification for volume-preserving Cartan actions of Γand G. Also, if G has real rank at least 3, we provide a C^\infty classification for volume-preserv…

The paper classifies actions of a specific group on certain manifolds.

Classifies cyclic actions on bordered surfaces up to topological conjugation.

In this paper I construct, using off the shelf components, a compact symplectic manifold with a non-trivial Hamiltonian circle action that admits no Kaehler structure. The non-triviality of the action is guaranteed by the existence of an isolated fixed point. The motivation for this work comes from the program of class…

An isometric action of a Lie group on a Riemannian manifold is of cohomogeneity one if the corresponding orbit space is one-dimensional. In this article we develop a conceptual approach to the classification of cohomogeneity one actions on Riemannian symmetric spaces of noncompact type in terms of orbit equivalence. As…

It is well-known by the work of Hsiang and Kleiner that every closed oriented positively curved 4-dimensional manifold with an effective isometric S^1-action is homeomorphic to S^4 or CP^2. As stated, it is a topological classification. The primary goal of this paper is to show that it is indeed a diffeomorphism classi…

New classification for curved manifolds with specific symmetries.

Classifies orbits of Hurwitz actions on dihedral quandles.

We give a complete classification of irreducible symmetric spaces for which there exist proper SL(2,R)-actions as isometries, using the criterion for proper actions by T. Kobayashi [Math. Ann. '89] and combinatorial techniques of nilpotent orbits. In particular, we classify irreducible symmetric spaces that admit surfa…

Classifies actions of SL(n,R) and SL(n,Z) on closed n-manifolds.

Cohomogeneity-one actions on symmetric spaces of mixed type

Classifies quotients of $S^n imes S^n$ by $\mathbb Z_{/p} imes \mathbb Z_{/p}$ actions.

We obtain a topological and weakly equivariant classification of closed three-dimensional Alexandrov spaces with an effective isometric circle action. As an application of the classification we prove a version of the Borel conjecture for closed three-dimensional Alexandrov spaces with circle symmetry.

The problem of equivariant rigidity is the $Γ$-homeomorphism classification of $Γ$-actions on manifolds with compact quotient and with contractible fixed sets for all finite subgroups of $Γ$. In other words, this is the classification of cocompact $E_{fin}Γ$-manifolds. We use surgery theory, algebraic $K$-theory, and t…

We study higher rank Cartan actions on compact manifolds preserving an ergodic measure with full support. In particular, we classify actions by $\R ^k$ with $k \geq 3$ whose one-parameter groups act transitively as well as nondegenerate totally nonsymplectic $\Zk$-actions for $k \geq 3$.

A robot learns to classify images with limited perception using a layered reinforcement learning approach.

Study of symplectomorphisms on ruled surfaces under circle actions.

In this paper, we give a weak classification of locally linear pseudofree actions of the cyclic group of order 3 on a $K3$ surface, and prove the existence of such an action which can not be realized as a smooth action on the standard smooth $K3$ surface.

We consider actions of Z^k, k \ge 2, by Anosov diffeomorphisms which are uniformly quasiconformal on each coarse Lyapunov distribution. These actions generalize Cartan actions for which coarse Lyapunov distributions are one-dimensional. We show that, under certain non-resonance assumptions on the Lyapunov exponents, a …

This paper classifies Hamiltonian actions by symplectic groupoids using Delzant subspaces.

We obtain the full classification of coisotropic and polar actions of compact Lie group on irreducible Hermitian symmetric spaces.

A survey of finite group actions on symplectic 4-manifolds is given with a special emphasis on results and questions concerning smooth or symplectic classification of group actions, group actions and exotic smooth structures, and homological rigidity and boundedness of group actions. We also take this opportunity to in…

Improves off-policy evaluation weights for balanced state-action pair distribution.

New groups defined that act on trees without repeating.

Classifies totally geodesic submanifolds and polar actions on Stiefel manifolds.

Improved multivariate time series classification models.

Study polar actions on Damek-Ricci spaces, proving existence and finding examples.

The paper calculates actions of string link operations for 4- and 5-component links.

The main result of the paper is the complete classification of the compact connected Lie groups acting coisotropically on complex Grassmannians. This is used to determine the polar actions on the same manifolds.

A new method recovers rewards from behavior policies using classification and regression.

We analyze polar actions on Hermitian and quaternion-Kähler symmetric spaces of compact type. For complex integrable polar actions on Hermitian symmetric spaces of compact type we prove a reduction theorem and several corollaries concerning the geometry of these actions. The results are independent of the classificatio…

Classifies circle actions on 6D manifolds with 4 fixed points.

Study free circle actions on specific 7-manifolds with positive Ricci curvature.

Classifies actions of groups on hyperbolic spaces, proving dichotomy.

We describe the orbit space of the action of the group $\mathrm{Sp}(2)\mathrm{Sp}(1)$ on the real Grassmann manifolds $\mathrm{Gr}_k(\mathbb{H}^2)$ in terms of certain quaternionic matrices of Moore rank not larger than $2$. We then give a complete classification of valuations on the quaternionic plane $\mathbb{H}^2$ w…

Classifies 3D spaces with circle actions, showing they are sums of manifolds and projective planes.

Classifies actions on Minkowski space up to orbit equivalence.