Related papers: The equivariant Spivak normal bundle and equivaria…

We introduce a notion of Poincar\'e duality for pairs of $\infty$-categories, extending Poincar\'e-Lefschetz duality for pairs of spaces. This categorical extension yields an efficient book-keeping device that affords, among other things, a…

An equivariant stable birational invariant of an action of a finite group on a smooth projective variety is the first cohomology group of the Picard module. Bogomolov-Prokhorov and Shinder computed this for actions of cyclic groups on…

We construct cup and cap products in intersection (co)homology with field coefficients. The existence of the cap product allows us to give a new proof of Poincare duality in intersection (co)homology which is similar in spirit to the usual…

It is proved that if $G$ is a compact Lie group, then an equivariant Serre fibration of $G$-CW-complexes is an equivariant Hurewicz fibration in the class of compactly generated $G$-spaces. In the nonequivariant setting, this result is due…

A careful account is given of generalized equivariant homology theories on the category of topological pairs acted on by a group. In particular, upon restriction to the category of equivariant simplicial complexes, the equivalence of…

Let G be a compact, connected and simply connected Lie group, and {\Omega}G the space of the loops in G based at the identity. This note shows a way to compute the cohomology of the total space of a principal {\Omega}G-bundle over a…

In this work, we prove that, under a topological condition, the cohomology associated with left-invariant elliptic structures on compact semisimple Lie groups can be computed using only left-invariant forms. This reduces the analytical…

For a closed Riemannian manifold $M$ with a compact Lie group $G$ acting by isometries, we show a generic multiplicity one theorem in equivariant min-max theory, and show in generic sense that there are infinitely many $G$-invariant minimal…

We study a new class of compact orientable manifolds, called big polygon spaces. They are intersections of real quadrics and related to polygon spaces, which appear as their fixed point set under a canonical torus action. What makes big…

An important ingredient in the completion theorem of equivariant K-theory given by S. Jackowski is that the representation ring R(Gamma) of a compact Lie group satisfies two restriction properties called (N) and (R\_{F}). We give in this…

Let g be a Lie bialgebra and let V be a finite-dimensional g-module. We study deformations of the symmetric algebra of V which are equivariant with respect to an action of the quantized enveloping algebra of g. In particular we investigate…

For any natural numbers $k \leq n$, the rational cohomology ring of the space of continuous maps $S^{2k-1} \to S^{2n-1}$ (respectively, $S^{4k-1} \to S^{4n-1}$) equivariant under the Hopf action of the circle (respectively, of the group…

We study Lie foliations on compact manifolds, in case the Lie group is compact. Our main results improve Tischler classical result on the existence of fibration and, as an application, we study the case the manifold has an amenable…

Here we prove a Poincar\'e-Verdier duality theorem for the o-minimal sheaf cohomology with definably compact supports of definably normal, definably locally compact spaces in an arbitrary o-minimal structure.

We study several duality isomorphisms between equivariant bivariant K-theory groups, generalising Kasparov's first and second Poincare duality isomorphisms. We use the first duality to define an equivariant generalisation of Lefschetz…

We compute (algebraically) the Euler characteristic of a complex of sheaves with constructible cohomology. A stratified Poincar\'e-Hopf formula is then a consequence of the smooth Poincar\'e-Hopf theorem and of additivity of the…

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,…

Let G be a locally compact group. We describe elements of KK^G (A,B) by equivariant homomorphisms, following Cuntz's treatment in the non-equivariant case. This yields another proof for the universal property of KK^G: It is the universal…

We describe the $G$-equivariant Grothendieck ring of a regular compactification $X$ of an adjoint symmetric space $G/H$ of minimal rank. This extends the results of Brion and Joshua for the equivariant Chow ring of wonderful symmetric…

For a finite group $G$, we compute the algebraic $K$-theory of the category of equivariant sheaves on a locally compact Hausdorff $G$-space, generalizing a result of Efimov, and determine the equivariant $E$-theory of the $C^*$-algebra of…