Related papers: The Hopf type theorem for equivariant gradient loc…

We study otopy classes of equivariant local maps and prove the Hopf type theorem for such maps in the case of a real finite dimensional orthogonal representation of a compact Lie group.

We prove that the inclusion of the space of gradient local maps into the space of all local maps from Hilbert space to itself induces a bijection between the sets of the respective otopy classes of these maps, where by a local map we mean a…

In this paper we develop a theory for constructing an invariant of closed oriented 3-manifolds, given a certain type of Hopf algebra. Examples are given by a quantised enveloping algebra of a semisimple Lie algebra, or by a semisimple…

We prove that homotopy invariants of finite degree distinguish homotopy classes of maps of a connected compact CW-complex to a nilpotent connected CW-complex with finitely generated homotopy groups.

The Hopf theorem states that homotopy classes of continuous maps from a closed connected oriented smooth $n$-manifold $M$ to the $n$-sphere are classified by their degree. Such a map is equivalent to a section of the trivial $n$-sphere…

For any finite-dimensional Hopf algebra $H$ we construct a group homomorphism $\biga(H)\to \text{BrPic}(\Rep(H))$, from the group of equivalence classes of $H$-biGalois objects to the group of equivalence classes of invertible exact…

Associated to any manifold equipped with a closed form of degree >1 is an `L-infinity algebra of observables' which acts as a higher/homotopy analog of the Poisson algebra of functions on a symplectic manifold. In order to study Lie group…

A natural extension of the Hopf-cyclic cohomology, with coefficients, is introduced to encompass topological Hopf algebras. The topological theory allows to work with infinite dimensional Lie algebras. Furthermore, the category of…

We define and study an equivariant version of Farber's topological complexity for spaces with a given compact group action. This is a special case of the equivariant sectional category of an equivariant map, also defined in this paper. The…

Following ideas of Graeme Segal, we construct an equivariant con- figuration space that is a model of equivariant connective K-homology spec- trum for finite groups, as a consequence we obtain an induction structure for equivariant…

Let $f,g:M \rightarrow N$ be two maps between simply-connected smooth manifolds $M$ and $N$, such that $M$ is compact and $N$ is of finite $\mathbb{R}$-type. The goal of this paper is to use integration of certain differential forms to…

For a given finite dimensional Hopf algebra $H$ we describe the set of all equivalence classes of cocycle deformations of $H$ as an affine variety, using methods of geometric invariant theory. We show how our results specialize to the…

We construct the vector space dual to the space of right-invariant differential forms construct from a first order differential calculus on inhomogeneous quantum group. We show that this vector space is equipped with a structure of a Hopf…

We define graded group schemes and graded group varieties and develop their theory. Graded group schemes are the graded analogue of group schemes and are in correspondence with graded Hopf algebra. In this setting, graded group varieties…

A bicovariant calculus of differential operators on a quantum group is constructed in a natural way, using invariant maps from \fun\ to \uqg\ , given by elements of the pure braid group. These operators --- the `reflection matrix' $Y \equiv…

The aim of this note is to prove the algebraic geometry analogue of the Invariant tubular neighborhood theorem which concerns the actions of compact Lie groups on smooth manifolds.

We compute the mapping class group orbits in the homotopy set of framings of a compact connected oriented surface with non-empty boundary. In the case $g > 1$ the computation is some modification of Johnson's results and certain arguments…

The results of a previous paper on the equivariant homotopy theory of crossed complexes are generalised from the case of a discrete group to general topological groups. The principal new ingredient necessary for this is an analysis of…

We define inductively a sequence of purely algebraic invariants - namely, classes in the Quillen cohomology of the Pi-algebra \pi_* X - for distinguishing between different homotopy types of spaces. Another sequence of such cohomology…

The first author's geometric Hopf invariant of a stable map $F:\Sigma^{\infty}X \to \Sigma^{\infty}Y$ is a stable ${\mathbb Z}_2$-equivariant map $h(F):\Sigma^{\infty}X \to \Sigma^{\infty}(Y \wedge Y)$ constructed by an explicit difference…