相关论文: Classification of locally standard torus actions

We study the lower bounds and upper bounds for LS-category and equivariant LS-category. In particular we compute both invariants for torus manifolds. There are some examples to show the sharpness of conditions in the theorems. Moreover the…

In this work, we study the Willmore submanifolds in a closed connected Riemannian manifold which are orbits for the isometric action of a compact connected Lie group. We call them homogeneous Willmore submanifolds or Willmore orbits. The…

We extend the methods of geometric invariant theory to actions of non--reductive groups in the case of homomorphisms between decomposable sheaves whose automorphism groups are non--reductive. Given a linearization of the natural action of…

This paper is concerned with the problem of stable diffeomorphism classification of 4-manifolds obtained using the surgery on loops. The main theorem states that under the assumption that the normal 1-type of two 4-manifolds in question is…

We study the global invariants of real analytic manifolds in the complex space with respect to the group of holomorphic unimodular transformations. We consider only totally real manifolds which admits a certain fibration over the circle. We…

We consider an irreducible Anosov automorphism L of a torus T^d such that no three eigenvalues have the same modulus. We show that L is locally rigid, that is, L is C^1 conjugate to any C^1-small perturbation f with the same periodic data.…

Let $G$ be the group of orientation-preserving isometries of a rank-one symmetric space $X$ of non-compact type. We study local rigidity of certain actions of a solvable subgroup $\Gamma \subset G$ on the boundary of $X$, which is…

We derive the moduli dependent threshold corrections to gauge couplings in toroidal orbifold compactifications. The underlying six dimensional torus lattice of the heterotic string theory is not assumed ---as in previous calculations--- to…

We consider compact manifolds $M$ with a cohomogeneity one action of a compact Lie group $G$ such that the orbit space $M/G$ is a closed interval. For $T$ a maximal torus of $G$, we find necessary and sufficient conditions on the group…

Given a symplectic manifold, we ask in how many different ways can a torus act on it. Classification theorems in equivariant symplectic geometry can sometimes tell that two Hamiltonian torus actions are inequivalent, but often they do not…

We discuss how the global geometry and topology of manifolds depend on different group actions of their fundamental groups, and in particular, how properties of a non-trivial compact 4-dimensional cobordism $M$ whose interior has a complete…

We present results and examples which show that the consideration of a certain tubular mutation is advantageous in the study of noncommutative curves which parametrize the simple regular representations of a tame bimodule. We classify all…

The smooth action of a compact Lie group on a compact manifold can be resolved to an iterated space, as made explicit by Pierre Albin and the second author. On the resolution the lifted action has fixed isotropy type corresponding to the…

In this paper, we compute the homotopy type of the group of equivariant symplectomorphisms of $S^2 \times S^2$ and $\mathbb{C}P^2 \# \overline{\mathbb{C}P^2}$ under the presence of Hamiltonian group actions of the circle $S^1$. We prove…

A principal toric bundle $M$ is a complex manifold equipped with a free holomorphic action of a compact complex torus $T$. Such a manifold is fibered over $M/T$, with fiber $T$. We discuss the notion of positivity in fiber bundles and…

We prove a criterion for an isometric action of a Lie group on a Riemannian manifold to be polar. From this criterion, it follows that an action with a fixed point is polar if and only if the slice representation at the fixed point is polar…

We prove that the Euler characteristic of an even-dimensional compact manifold with positive (nonnegative) sectional curvature is positive (nonnegative) provided that the manifold admits an isometric action of a compact Lie group $G$ with…

We show that if a compact K\"ahler manifold admits a weighted extremal metric for the action of a torus, so too does its blowup at a relatively stable point that is fixed by both the torus action and the extremal field. This generalises…

Discrete, unimodular inclusions of factors $(N\subseteq M, E)$ with $N$ of type $\rm{II}_{1}$ have a natural notion of standard invariant, generalizing the finite index case. When the unitary tensor category of $N$-$N$ bimodules generated…

We show that, up to topological conjugation, the equivalence class of a Morse-Smale diffeomorphism without heteroclinic curves on 3-manifold is completely defined by an em- bedding of two-dimensional stable and unstable heteroclinic…