Related papers: Topology of generalized complex quotients

A generalized moment map is proposed for arbitrary symplectic actions of compact connected Lie groups on closed symplectic manifolds, in the spirit of the circle -valued maps introduced by D. McDuff in the case of non-Hamiltonian circle…

We develop a set of sufficient conditions for guaranteeing that an integrable system with a symmetry group $K$ on a manifold $M$ descends to an integrable system on a dense open subset of the quotient Poisson space $M/K$. The higher…

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…

In this article we introduce flag Bott manifolds of general Lie type as the total spaces of iterated flag bundles. They generalize the notion of flag Bott manifolds and generalized Bott manifolds, and admit nice torus actions. We calculate…

We prove that the GKM graphs of GKM$_4$ manifolds that are either Hamiltonian or of complexity one extend to torus graphs. The arguments are based on a reformulation of the extension problem in terms of a natural representation of the…

We show that for any cohomogeneity one continuous action of a compact connected Lie group $G$ on a closed topological manifold the equivariant cohomology equipped with its canonical $H^*(BG)$-module structure is Cohen-Macaulay. The proof…

We introduce the notion of equivariant basic cohomology for singular Riemannian foliations with transverse infinitesimal actions, and prove some elementary properties such as its invariance under homotopies. For the particular case of…

We show that symplectic forms taming complex structures on compact manifolds are related to special types of almost generalized K\"ahler structures. By considering the commutator $Q$ of the two associated almost complex structures…

In this paper, we do the two things. 1. We present a formula to compute the rational cohomology ring of a real topological toric manifold, and thus that of a small cover or a real toric manifold, which implies the formula of Suciu and…

Using the language of T-varieties, we study torus invariant curves on a complete normal variety $X$ with an effective codimension-one torus action. In the same way that the $T$-invariant Weil divisors on $X$ are sums of "vertical" divisors…

We show that the cohomology algebra of the complement of a coordinate subspace arrangement in m-dimensional complex space is isomorphic to the cohomology algebra of Stanley-Reisner face ring of a certain simplicial complex on m vertices.…

We study fixed points of smooth torus actions on closed manifolds using fixed point formulas and equivariant elliptic genera. We also give applications to positively curved Riemannian manifolds with symmetry.

The Chow quotient of a projective variety by the action of a complex torus is known to have a very complicated geometry, even in the case of simple varieties, such as rational homogeneous varieties. In this paper we propose an approach in…

An action of a complex reductive group $\mathrm G$ on a smooth projective variety $X$ is regular when all regular unipotent elements in $\mathrm G$ act with finitely many fixed points. Then the complex $\mathrm G$-equivariant cohomology…

We explore the consequences of curvature and torsion on the topology of quaternionic contact manifolds with integrable vertical distribution. We prove a general Myers theorem and establish a Cartan-Hadamard result for almost qc-Einstein…

Let $S$ and $T$ be smooth projective varieties over an algebraically closed field. Suppose that $S$ is a surface admitting a decomposition of the diagonal. We show that, away from the characteristic of $k$, if an algebraic correspondence $T…

Let $M^{2d}$ be a compact symplectic manifold and $T$ a compact $n$-dimensional torus. A Hamiltonian action, $\tau$, of $T$ on $M$ is a GKM action if, for every $p \in M^T$, the isotropy representation of $T$ on $T_pM$ has pair-wise…

We show that the theory of stable complex $G$-cobordisms, for a torus $G$, is embedded into the theory of stable complex $G$-cobordisms of not necessarily compact manifolds equipped with proper abstract moment maps. Thus the introduction of…

In this paper we study a specific class of actions of a $2$-torus $\mathbb{Z}_2^k$ on manifolds, namely, the actions of complexity one in general position. We describe the orbit space of equivariantly formal $2$-torus actions of complexity…

GKM theory is a powerful tool in equivariant topology and geometry that can be used to generalize classical ideas from (quasi)toric manifolds to more general torus actions. After an introduction to the topic this survey focuses on recent…