Related papers: A Spectral Sequence for Equidimensional Actions of…

For manifolds equipped with group actions, we have the following natural question: To what extent does the equivariant cohomology determine the equivariant diffeotype? We resolve this question for Hamiltonian circle actions on compact,…

We show that a compact representation of a semisimple Lie group has an orthogonal decomposition into finite length representations. This generalises and simplifies a number of more special spectral theorems in the literature. We apply it to…

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…

For a compact Riemannian manifold $M^{n+1}$ acted isometrically on by a compact Lie group $G$ with cohomogeneity ${\rm Cohom}(G)\geq 2$, we show the Weyl asymptotic law for the $G$-equivariant volume spectrum. As an application, we show in…

The space of realizations of a finite-dimensional Lie algebra by first order differential operators is naturally isomorphic to H^1 with coefficients in the module of functions. The condition that a realization admits a finite-dimensional…

Studies the cohomology of p-central, powerful, p-groups with a certain extension property. These groups are naturally associated to Lie algebras. The paper develops a machinery that calculates the first few terms of the Bockstein spectral…

It is shown that the Mayer-Vietoris sequence holds for the cohomology of complexes of Lie algebroids which are defined on simplicial complexes and satisfy the compatibility condition concerning restrictions to the faces of each simplex. The…

We build a spectral sequence converging to the cohomology of a fusion system with a strongly closed subgroup. This spectral sequence is related to the Lyndon-Hochschild-Serre spectral sequence and coincides with it for the case of an…

We construct models for the classifying spaces of coabelian subgroups of right-angled Coxeter groups as homotopy orbit spaces of real moment-angle complexes, generalizing well-known models for the classifying space of a right-angled Coxeter…

In the paper we describe complexes whose homologies are naturally isomorphic to the first term of the Vassiliev spectral sequence computing (co)homology of the spaces of long knots in R^d, d>=3. The first term of the Vassiliev spectral…

In this paper, we examine Lie group actions on moduli spaces (sets themselves built as quotients by group actions) and their fixed points. We show that when the Lie group is compact and connected, we obtain a linear constraint. This…

Let $\mathcal{G}$ be a bundle gerbe with connection on a smooth manifold $M$, and let $\rho: G \rightarrow \operatorname{Diff}(M)$ be a smooth action of a Fr\'echet--Lie group $G$ on $M$ that preserves the isomorphism class of…

We determine the action of the Torelli group on the equivariant cohomology of the space of flat SL(2,C) connections on a closed Riemann surface. We show that the trivial part of the action contains the equivariant cohomology of the even…

This is the first of a series of papers dealing with the asymptotic behavior of certain integrals occuring in the description of the spectrum of an invariant elliptic operator on a compact Riemannian manifold carrying the action of a…

The present paper links the representation theory of Lie groupoids and infinite-dimensional Lie groups. We show that smooth representations of Lie groupoids give rise to smooth representations of associated Lie groups. The groups envisaged…

For Riemannian submersions with fibers of basic mean curvature, we compare the spectrum of the total space with the spectrum of a Schr\"{o}dinger operator on the base manifold. Exploiting this concept, we study submersions arising from…

For a Lie groupoid $\mathcal{G}$ with Lie algebroid $A$, we realize the symplectic leaves of the Lie-Poisson structure on $A^*$ as orbits of the affine coadjoint action of the Lie groupoid $\mathcal{J}\mathcal{G}\ltimes T^*M$ on $A^*$,…

We define a spectral flow for paths of selfadjoint Fredholm operators that are equivariant under the orthogonal action of a compact Lie group as an element of the representation ring of the latter. This $G$-equivariant spectral flow shares…

Poincare duality lies at the heart of the homological theory of manifolds. In the presence of the action of a group it is well-known that Poincare duality fails in Bredon's ordinary, integer-graded equivariant homology. We give here a…

The aim of this paper is to classify the cohomogeneity one conformal actions on the three-dimensional essential Riemannian spaces, up to orbit equivalence. Among other results, the representations of all connected Lie groups acting with…