Related papers: Topology of generalized complex quotients

We extend the famous convexity theorem of Atiyah, Guillemin and Sternberg to the case of non-Hamiltonian actions. We show that the image of a generalized momentum map is a bounded polytope times a vector space. We prove that this picture is…

Let M be a spin manifold with a circular action. Given an elliptic curve E, we introduce, as in Grojnowski, elliptic bouquets of germs of holomorphic equivariant cohomology classes on M. Following Bott-Taubes and Rosu, we show that…

Quoric manifolds are the quaternionic analogue of toric manifolds. They admit a locally nice action of $(S^3)^n$ and the quotient is a manifold with corners. We show that they satisfy equivariant rigidity. More precisely, any locally linear…

Let G be a compact, connected Lie group, acting smoothly on a manifold M. Goresky-Kottwitz-MacPherson described a small Cartan model for the equivariant cohomology of M, quasi-isomorphic to the standard Cartan complex of equivariant…

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.…

We determine conditions under which two Hamiltonian torus actions on a symplectic manifold $M$ are homotopic by a family of Hamiltonian torus actions, when $M$ is a toric manifold and when $M$ is a coadjoint orbit.

Let $T$ be a compact torus. We prove that, up to equivariant rational equivalence, the category of $T$-simply connected, $T$-finite type $T$-spaces with finitely many isotropy types is completely described by certain finite systems of…

A torus manifold is a closed smooth manifold of dimension $2n$ having an effective smooth $T^n = (S^1)^n$-action with non-empty fixed points. Petrie \cite{petrie:1973} has shown that any homotopy equivalence between a complex projective…

Let G be a compact connected Lie group, and (M,\omega) a Hamiltonian G-space with proper moment map \mu. We give a surjectivity result which expresses the K-theory of the symplectic quotient M//G in terms of the equivariant K-theory of the…

This is a sequel of \cite{Wang}, which provides a general formalism for this paper. We mainly investigate thoroughly a subclass of toric generalized K$\ddot{a}$hler manifolds of symplectic type introduced by Boulanger in \cite{Bou}. We find…

In this paper, we consider generalized moment maps for Hamiltonian actions on $H$-twisted generalized complex manifolds introduced by Lin and Tolman \cite{Lin}. The main purpose of this paper is to show convexity and connectedness…

Let $M$ be a compact, connected symplectic manifold with a Hamiltonian action of a compact $n$-dimensional torus $T$. Suppose that $M$ is equipped with an anti-symplectic involution $\sigma$ compatible with the $T$-action. The real locus of…

For T an abelian compact Lie group, we give a description of T-equivariant K-theory with complex coefficients in terms of equivariant cohomology. In the appendix we give applications of this by extending results of Chang-Skjelbred and…

Let $G$ be a complex Lie group acting on a compact complex Hermitian manifold $M$ by holomorphic isometries. We prove that the induced action on the Dolbeault cohomology and on the Bott-Chern cohomology is trivial. We also apply this result…

Let G be a subgroup of finite index in SL(n,Z) for N > 4. Suppose G acts continuously on a manifold M, with fundamental group Z^n, preserving a measure that is positive on open sets. Further assume that the induced G action on H^1(M) is…

Let $X$ be a torus manifold with locally standard action of a compact torus $T$ of half the dimension and orbit space a homology polytope. Smooth complete complex toric varieties and quasi-toric manifolds are examples of torus manifolds.…

Let X be a smooth simplicial toric variety. Let Z be the set of T-fixed points of X. We construct a filtration for A(Z), the ring of complex-valued functions on Z, such that Gr A(Z) is isomorphic to the cohomology algebra of X. This is the…

A twist is a datum playing a role of a local system for topological $K$-theory. In equivariant setting, twists are classified into four types according to how they are realized geometrically. This paper lists the possible types of twists…

This note is an addendum to our earlier work \cite{humi}. In \cite{humi}, we studied a Hamiltonian action for a generalized Calabi-Yau manifold and showed that the Duistermaat-Heckman theorem holds. The purpose of this note is to show that…

Given a torus action on a compact space X, a fundamental result of Borel and Atiyah-Segal asserts that the equivariant cohomology of X is concentrated in the fixed locus X^T, up to inverting enough Chern classes. We prove an analogue for…