Related papers: Gromov's Oka principle for equivariant maps

The problem of equivariant rigidity is the $\Gamma$-homeomorphism classification of $\Gamma$-actions on manifolds with compact quotient and with contractible fixed sets for all finite subgroups of $\Gamma$. In other words, this is the…

We show that (equivariant) K-theoretic 3-point Gromov-Witten invariants of genus zero on a Grassmann variety are equal to triple intersections computed in the ordinary (equivariant) K-theory of a two-step flag manifold, thus generalizing an…

We formulate a quantization commutes with reduction principle in the setting where the Lie group $G$, the symplectic manifold it acts on, and the orbit space of the action may all be noncompact. It is assumed that the action is proper, and…

Let $G$ be a compact, connected, and simply-connected Lie group, equipped with an anti-involution $a_G$ which is the composition of a Lie group involutive automorphism $\sigma_G$ and the group inversion. We view $(G, a_G)$ as a Real $(G,…

An orbifold is a topological space modeled on quotient spaces of a finite group actions. We can define the universal cover of an orbifold and the fundamental group as the deck transformation group. Let $G$ be a Lie group acting on a space…

In equivariant topology, Greenlees and May used Mackey functors to show that, rationally, the stable homotopy category of $G$-spectra over a finite group $G$ splits as a product of simpler module categories. We extend the algebraic part…

An algebraic GKM manifold is a non-singular algebraic variety equipped with an algebraic action of an algebraic torus, with only finitely many torus fixed points and finitely many 1-dimensional orbits. In this expository article, we use…

Let $G$ be an affine algebraic group over an algebraically closed field $k$ of characteristic zero. In this paper, we consider finite $G$-equivariant morphisms $F:X\to Y$ of irreducible affine $G$-varieties. First we determine under which…

A group action on the input ring or category induces an action on the algebraic $K$-theory spectrum. However, a shortcoming of this naive approach to equivariant algebraic $K$-theory is, for example, that the map of spectra with $G$-action…

For G a complex reductive group and X a smooth projective or convex quasi-projective polarized G-variety we construct a formal map in quantum K-theory from the equivariant quantum K-theory $QK^G(X)$ to the quantum K-theory of the git…

In this paper, we show that general homogeneous manifolds $G/P$ satisfy Conjecture $\mathcal{O}$ of Galkin, Golyshev and Iritani which `underlies' Gamma conjectures I and II of them. Our main tools are the quantum Chevalley formula for…

We construct equivariant $KK$-theory with coefficients in $\mathbb{R}$ and $\mathbb{R}/\mathbb{Z}$ as suitable inductive limits over ${\rm II}_1$-factors. We show that the Kasparov product, together with its usual functorial properties,…

Let X=G/P be a homogeneous space and e_k be the class of a simple coroot in H_2(X). A theorem of Strickland shows that for almost all X, the variety of pointed lines of degree e_k, denoted Z_k(X), is again a homogeneous space. For these X…

For a finite group G acting on a smooth projective variety X, we construct two new G-equivariant rings: first the stringy K-theory of X, and second the stringy cohomology of X. For a smooth Deligne-Mumford stack Y we also construct a new…

Let G=SU(2) and let \Omega G denote the space of continuous based loops in G, equipped with the pointwise conjugation action of G. It is a classical fact in topology that the ordinary cohomology H^*(\Omega G) is a divided polynomial algebra…

Let $k$ be a field, let $G$ be a reductive algebraic group over $k$, and let $V$ be a linear representation of $G$. Geometric invariant theory involves the study of the $k$-algebra of $G$-invariant polynomials on $V$, and the relation…

For an orbifold X which is the quotient of a manifold Y by a finite group G we construct a noncommutative ring with an action of G such that the orbifold cohomology of X as defined in math.AG/0004129 by Chen and Ruan is the G invariant…

Let $G$ be a compact, connected, and simply-connected Lie group, equipped with a Lie group involution $\sigma_G$ and viewed as a $G$-space with the conjugation action. In this paper, we present a description of the ring structure of the…

We first introduce an invariant index for G-equivariant elliptic differential operators on a locally compact manifold M admitting a proper cocompact action of a locally compact group G. It generalizes the Kawasaki index for orbifolds to the…

For a closed Riemannian manifold $M$ with a compact Lie group $G$ acting by isometries, we show that there are infinitely many $G$-invariant minimal hypersurfaces. Under the assumption that $M$ contains at most a finite number of minimal…