Related papers: Spectral sequence of an isometric action

We determine all natural operations and their relations on the homotopy groups of spectral partition Lie algebras, which coincide with $\mathbb{F}_p$-linear topological Andr\'{e}-Quillen cohomology operations at any prime. We construct…

Let M be a compact simply connected hyperk\"ahler (or holomorphically symplectic) manifold, \dim H^2(M)=n. Assume that M is not a product of hyperkaehler manifolds. We prove that the Lie algebra so(n-3,3) acts by automorphisms on the…

The chiral equivariant cohomology contains and generalizes the classical equivariant cohomology of a manifold M with an action of a compact Lie group G. For any simple G, there exist compact manifolds with the same classical equivariant…

By recent work on some conjectures of Pillay, each definably compact group $G$ in a saturated o-minimal expansion of an ordered field has a normal ``infinitesimal subgroup'' $G^{00}$ such that the quotient $G/G^{00}$, equipped with the…

We show that for a Hamiltonian action of a compact torus $G$ on a compact, connected symplectic manifold $M$, the $G$-equivariant cohomology is determined by the residual $S^1$ action on the submanifolds of $M$ fixed by codimension-1 tori.…

A typical example of a Cartan calculus consists of the Lie derivative and the contraction with vector fields of a manifold on the derivation ring of the de Rham complex. In this manuscript, a second stage of the Cartan calculus is…

Let $M$ be a closed connected smooth manifold and $G=\textmd{Diff}_0(M)$ denote the connected component of the diffeomorphism group of $M$ containing the identity. The natural action of $G$ on $M$ induces the trace homomorphism on homology.…

Given a compact Riemannian manifold $(M g)$ and Morse function $f:m\to \mathbb{R}$ whose gradient flow satisfies the Morse-Smale condition, (i.e. the stable and unstable manifolds of f intersect transversely) we construct a chain complex…

Consider the mod 2 homology spectral sequence associated to a cosimplicial space X. We construct external operations whose target is the spectral sequence associated to E\Sigma_2 \times_{\Sigma_2} (X\times X). If X is a cosimplicial…

We show that the category of free rational G-spectra for a connected compact Lie group G is Quillen equivalent to the category of torsion differential graded modules over the polynomial cohomology ring on the classifying space, H*(BG). The…

If a closed smooth manifold $M$ with an action of a torus $T$ satisfies certain conditions, then a labeled graph $\mG_M$ with labeling in $H^2(BT)$ is associated with $M$, which encodes a lot of geometrical information on $M$. For instance,…

We extend the work of Allday-Franz-Puppe on syzygies in equivariant cohomology from tori to arbitrary compact connected Lie groups G. In particular, we show that for a compact orientable G-manifold X the analogue of the Chang-Skjelbred…

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…

Let $\varphi$ and $\varphi'$ be two homotopic actions of the topological group $G$ on the topological space $X$. To an object $A$ in the $G$-equivariant derived category $D_{\varphi}(X)$ of $X$ relative to the action $\varphi$ we associate…

Let $(M,\omega)$ be a compact symplectic manifold with a Hamiltonian GKM action of a compact torus. We formulate a positive condition on the space; this condition is satisfied if the underlying symplectic manifold is monotone. The main…

We show by studying the symplectic geometry of the extended moduli space that the intersection cohomology of the representation space $Hom(\pi_1(\Sigma),G)/G$ for a simply connected compact Lie group $G$ is naturally embedded into the $G$…

Given a symmetric triple $(G,K,\sigma)$ of compact type, with $G^{\sigma} = K$, the well known Cartan embedding $\hat{\Phi}: G/K \to G$ homothetically embeds the symmetric space $M = G/K$ as a totally geodesic submanifold of $G$. In this…

Let $M$ be a pseudo-Hermitian homogeneous space of finite volume. We show that $M$ is compact and the identity component $G$ of the group of holomorphic isometries of $M$ is compact. If $M$ is simply connected, then even the full group of…

For any abelian compact Lie group $G$, we introduce a family of $G$-stratified pseudomanifolds, whose main feature is the preservation of the orbit spaces in the category of stratified pseudomanifolds. Which generalize a previous definition…

We present a simple proof of a precise version of the localization theorem in equivariant cohomology. As an application, we describe the cohomology algebra of any compact symplectic variety with a multiplicity-free action of a compact Lie…