Related papers: Equivariant complex structures on homogeneous spac…

We consider compact homogeneous spaces G/H of positive Euler characteristic endowed with an invariant almost complex structure J and the canonical action \theta of the maximal torus T ^{k} on G/H. We obtain explicit formula for the…

The aim of this paper is to study further the universal toric genus of compact homogeneous spaces and their homogeneous fibrations. We consider the homogeneous spaces with positive Euler characteristic. It is well known that such spaces…

Considering the potential equivariant formality of the left action of a connected Lie group $K$ on the homogeneous space $G/K$, we arrive through a sequence of reductions at the case $G$ is compact and simply-connected and $K$ is a torus.…

This paper shows that the integral equivariant cohomology Chern numbers completely determine the equivariant geometric unitary bordism classes of closed unitary $G$-manifolds, which gives an affirmative answer to the conjecture posed by…

Let $G$ be a compact connected Lie group and $K$ a closed connected subgroup. Assume that the order of any torsion element in the integral cohomology of $G$ and $K$ is invertible in a given principal ideal domain $k$. It is known that in…

Let $G$ be a compact connected Lie group and $T$ be its maximal torus. The homogeneous space $G/T$ is called the (complete) flag manifold. One of the main goals of the {\em equivariant Schubert calculus} is to study the $T$-equivariant…

Let G be a compact connected Lie group with maximal torus T, and H a closed subgroup containing T . We work out the Atiyah--Bott--Berline--Vergne localization formula for the homogeneous space G/H under the natural action of the maximal…

Let G be a finite dimensional simple complex group equipped with the standard Poisson Lie group structure. We show that all G-homogeneous (holomorphic) Poisson structures on $G/H$, where $H \subset G$ is a Cartan subgroup, come from…

In this paper we first consider the Hamiltonian action of a compact connected Lie group on an $H$-twisted generalized complex manifold $M$. Given such an action, we define generalized equivariant cohomology and generalized equivariant…

Let $X$ be a topological space upon which a compact connected Lie group $G$ acts. It is well-known that the equivariant cohomology $H_G^*(X;\Q)$ is isomorphic to the subalgebra of Weyl group invariants of the equivariant cohomology…

The rational Borel equivariant cohomology for actions of a compact connected Lie group is determined by restriction of the action to a maximal torus. We show that a similar reduction holds for any compact Lie group $G$ when there is a…

We extend work of Davis and Januszkiewicz by considering {\it omnioriented} toric manifolds, whose canonical codimension-2 submanifolds are independently oriented. We show that each omniorientation induces a canonical stably complex…

We consider the action of a noncompact torus H on the compact quotient G/L, where G is a Lie group containing H and L is a uniform lattice in G. Using harmonic analysis on G we prove a formula relating the compact orbits of H to the action…

Let $G$ be a compact Lie group with a maximal torus $T$. Based on a presentation of the integral cohomology ring $H^{\ast}(G/T)$ of the flag manifold $G/T$ in \cite{DZ1}we have presented in \cite{DZ2}an explicit and unified construction of…

We restrict geometric tangential equivariant complex $T^n$-bordism to torus manifolds and provide a complete combinatorial description of the appropriate non-commutative ring. We discover, using equivariant $K$-theory characteristic…

We use equivariant localization and divided difference operators to determine formulas for the torus-equivariant fundamental cohomology classes of $K$-orbit closures on the flag variety $G/B$, where $G = GL(n,\C)$, and where $K$ is one of…

We partially describe equivariant Dirac and generalized complex structures on a homogeneous space $G/K$ by giving equivalent data involving only the Lie algebra. We consider real semisimple adjoint orbits in any semisimple Lie algebra over…

Consider the space Hom(Z^n,G) of pairwise commuting n-tuples of elements in a compact Lie group G. This forms a real algebraic variety, which is generally singular. In this paper, we construct a desingularization of the generic component of…

The subject of this dissertation is the Gysin homomorphism in equivariant cohomology for spaces with torus action. We consider spaces which are quotients of classical semisimple complex linear algebraic groups by a parabolic subgroup with…

We study the equivariant cobordism rings for the action of a torus $T$ on smooth varieties over an algebraically closed field of characteristic zero. We prove a theorem describing the rational $T$-equivariant cobordism rings of smooth…