Related papers: Functoriality of equivariant eta forms

We give an explicit, positive, and type-uniform formula for all equivariant structure constants of the Peterson Schubert calculus in arbitrary Lie types, using only the Cartan matrix of the corresponding root system $\Phi$. This solves an…

In this thesis we study two main topics which culminate in a proof that four distinct definitions of the equivariant derived category of a smooth algebraic group $G$ acting on a variety $X$ are in fact equivalent. In the first part of this…

Let $X$ be a partial flag variety, equipped with the Borel action by multiplication. We give a criterion for the equivariant derived category with modular coefficients to be formal.

For a Lie group G, we seek the right definition of a "moment space" for G. One axiom is clear, involving a closed equivariant three-form. We construct this form for symmetric spaces associated to a symmetric pair (H,G) with an additional…

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…

We find presentations by generators and relations for the equivariant quantum cohomology of the Grassmannian. For these presentations, we also find determinantal formulae for the equivariant quantum Schubert classes. To prove this, we use…

We make explicit Poincar\'{e} duality for the equivariant $K$-theory of equivariant complex projective spaces. The case of the trivial group provides a new approach to the $K$-theory orientation.

We construct a 2-category version of tom Dieck's equivariant fundamental groupoid for representable orbifolds and show that the discrete fundamental groupoid is Morita invariant; hence an orbifold invariant for representable orbifolds.

We study (pre-)sheaves in bicategories on geometric categories: smooth manifolds, manifolds with a Lie group action and Lie groupoids. We present three main results: we describe equivariant descent, we generalize the plus construction to…

We show that the Morse complex of a compact Lie monoid can be given the structure of an $f$-bialgebra, a chain-level version of bialgebras introduced in [CHM24]; and that this assignment defines an $\infty$-functor. As a consequence, we…

We characterize Carnot groups admitting a 1-quasiconformal metric inversion as the Lie groups of Heisenberg type whose Lie algebras satisfy the $J^2$-condition, thus characterizing a special case of inversion invariant bi-Lipschitz…

Let $\frak g$ be the finite dimensional simple Lie algebra associated to an indecomposable and symmetrizable generalized Cartan matrix $C=(a_{ij})_{n\times n}$ of finite type and let $\frak d$ be a finite dimensional Lie algebra related to…

In this note we present an analogue of equivariant formality in $K$-theory and show that it is equivalent to equivariant formality \emph{\`a la} Goresky-Kottwitz-MacPherson. We also apply this analogue to give alternative proofs of…

We consider a class of linear ODEs of second order with variable coefficients and construct its Lie algebra of Lie group of equivalence transformations. Further we find invariants and differential invariants of this Lie algebra and by using…

We introduce a practical construction of group-equivariant and permutation-invariant functions of $N$ variables given a finite-dimensional space stable with respect to the group action. The construction applies to any connected linear Lie…

This paper is a continuation of "Quantization of Lie bialgebras, I" (q-alg/9606005). We show that the quantization procedure defined in "Quantization of Lie bialgebras, I" is given by universal acyclic formulas and defines a functor from…

Problems of dense and closed extension of actions of compact transformation groups are solved. The method developed in the paper is applied to problems of extension of equivariant maps and of construction of equivariant compactifications.

The bicovariant differential calculus on the three-dimensional Kappa-Poincar'e group and the corresponding Lie-algebra structure are described. The equivalence of this Lie-algebra structure and the three-dimensional $\kappa$-Poincar\'e…

This is a continuation of the authors' previous work [math.AT/9910001] on classification of equivariant complex vector bundles over a circle. In this paper we classify equivariant real vector bundles over a circle with a compact Lie group…

In this work we obtain the general form of polynomial mappings that commute with a linear action of a relative symmetry group. The aim is to give results for relative equivariant polynomials that correspond to the results for relative…