Related papers: Equivariant torsion and G-CW-complexes

This note surveys the well-known structure of G-manifolds and summarizes parts of two papers that have not yet appeared in print: one with joint with J. Bruning and F. W. Kamber, and another with I. Prokhorenkov. In particular, from a given…

On a smooth closed oriented $4$-manifold $M$ with a smooth action of a finite group $G$ on a Spin$^c$ structure, $G$-monopole invariant is defined by "counting" $G$-invariant solutions of Seiberg-Witten equations for any $G$-invariant…

We discuss general properties of strong G$_2$-structures with torsion and we investigate the twisted G$_2$ equation, which represents the G$_2$-analogue of the twisted Calabi-Yau equation for SU$(n)$-structures introduced by…

We continue our investigation of versality for parametrized families of linear retarded functional differential equations (RFDEs) projected onto finite-dimensional invariant manifolds. In this paper, we consider RFDEs equivariant with…

We consider a consider the case of a compact manifold M, together with the following data: the action of a compact Lie group H and a smooth H-invariant distribution E, such that the H-orbits are transverse to E. These data determine a…

We give an abstract version of the hard Lefschetz theorem, the Lefschetz decomposition and the Hodge-Riemann theorem for compact Kaehler manifolds.

Let M be a manifold carrying the action of a Lie group G, and A a Lie algebroid on M equipped with a compatible infinitesimal G-action. Out of these data we construct an equivariant Lie algebroid cohomology and prove for compact G a related…

We prove the Hodge-Riemann bilinear relations, the hard Lefschetz theorem and the Lefschetz decomposition for compact Kahler manifolds in the mixed situation.

We construct an equivariant L-class for orientation preserving actions of a compact Lie group on a Whitney stratified compact oriented pseudomanifold that satisfies the Witt condition, for example on a compact pure-dimensional complex…

We describe a geometric compactification of the moduli stack of left invariant complex structures on a fixed real Lie group or a fixed quotient. The extra points are CR structures transverse to a real foliation.

This paper is devoted to the development and applications of some (new) basic concepts in Lie theory, both from `computational" and "observability" viewpoint. We specify set of all "G-equivariant" maps from a given Lie group G to the…

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…

Let $\Gamma$ be a finite group acting on a Lie group $G$. We consider a class of group extensions $1 \to G \to \hat{G} \to \Gamma \to 1$ defined by this action and a $2$-cocycle of $\Gamma$ with values in the centre of $G$. We establish and…

Invariant connections with torsion on simple group manifolds $S$ are studied and an explicit formula describing them is presented. This result is used for the dimensional reduction in a theory of multidimensional gravity with curvature…

The long-standing problem of the perfectness of the compactly supported equivariant homeomorphism group on a $G$-manifold (with one orbit type) is solved in the affirmative. The proof is based on an argument different than that for the case…

We give a short introduction to the theory of twisted Alexander polynomials of a 3--manifold associated to a representation of its fundamental group. We summarize their formal properties and we explain their relationship to twisted…

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…

We consider homogeneous hypercomplex manifolds with a transitive action of a compact Lie group and we give a characterization of invariant HKT metrics on them. On every such hypercomplex manifold we prove the existence of an invariant…

We study G-invariant Kaehler metrics on G^C from the Hamiltonian point of view. As an application we show that there exist (GxG)-invariant Ricci-flat Kaehler metrics on G^C for any compact semisimple Lie group G.

Let G be a locally compact group, let X be a universal proper G-space, and let Z be a G-equivariant compactification of X that is H-equivariantly contractible for each compact subgroup H of G. Let W be the resulting boundary. Assuming the…