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### cohomology of the orbit space of a group action

Let $M$ be a manifold. Let a finite group $G$ act on $M$ discretely. Let $F$ be a field. Suppose the induced action of $G$ on the cohomology algebra $H^*(M,F)$ is known. We want to obtain $H^*(M/G;F)$...
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### fixpoint algebras of a permutation action

Let $D$ be an infinite UHF algebra, e.g. the infinite tensor product of the matrix algebra $M_k(\mathbb{C})$. The permutation group $\Sigma_n$ acts on the $n$-fold tensor product $D^{\otimes n}$ in a ...
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### Is the quotient of a scheme by the free action of an elliptic curve an algebraic space?

Let $X$ be a scheme (I'm happy to assume that $X$ is of finite type, separated, and over $\mathbb{C}$) and let $E$ be an elliptic curve which acts freely on $X$. Does the quotient stack $[X/E]$ have ...
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### Is there a faithful transitive locally finite action of the modular group?

Is there a faithful transitive action of $G = \mathrm{PSL}_2(\mathbb{Z})$ on $\mathbb{Z}$ such that orbits under each $g \in G$ are finite?
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I hope someone can help me with this. Let $X$ be a smooth projective variety, say over the complex numbers and let $Z$ be a closed subvariety of $X$. Assume that $X$ is acted upon by a finite group $... 2answers 228 views ### A natural bijection between the orbit spaces of$p$-nilpotent matrices for varying$p$Let$k$be an algebraically closed field of characteristic$p$, call a matrix$X\in\mathfrak{gl}_n(k)p$-nilpotent if$X^p=0$, and let$\mathcal{N}_1=\mathcal{N}_1(\mathfrak{gl}_n(k))$be the set of ... 1answer 111 views ### Subgroups of$E(n) = \mathbb{R}^n \rtimes O(n)$with trivial orbit space Let G be a subgroup of$E(n) = \mathbb{R}^n \rtimes O(n)$(the rigid motions of$\mathbb{R}^n$) with orbit space as a point. Example: the group of all translations of$\mathbb{R}^n$and of course any ... 1answer 82 views ### 'Convex' slices of proper actions Consider a Lie group$G$acting properly on a manifold$M$. Then by the slice theorem we can find for any point$m\in M$a submanifold transverse to the orbit$\mathcal{O}$through$m$and which is (... 2answers 322 views ### Action of Mapping Class Group on Arc complex Suppose$S$is a surface of finite type with nonempty boundary. Now consider the arc complex$\mathcal{A}$. The action of Mod(S)(mapping class group) on the set of all vertices has finitely many ... 1answer 626 views ### When taking the fixed points commutes with taking the orbits Let$G$and$H$be groups, both acting on a set$X$on the left, in such a way that the two actions commute. (Equivalently, let$G \times H$act on$X$.) The set$\text{Fix}_H(X)$of$H$-fixed ... 1answer 661 views ### Orbits of group scheme action I am interested in orbits of the action of a group scheme on a scheme and I'm particularly interested in the following special case: Let$k$be an algebraically closed field, let$G$be an affine ... 0answers 152 views ### Diffeomorphism between open annuli preserving common symmetries Suppose$A$and$B$are subsets of$\mathbb{R}^2$homeomorphic (and thus$C^\infty$diffeomorphic) to the open annulus (punctured$\mathbb{B}^2$) and let$G$be the group of isometries of${\mathbb R}^...
Let $G$ be a discrete group acting on a compact metric space $X$. A point $x\in X$ is called a limit point, if there is a base point $x_0\in X$ and an injective sequence $(x_k)_{k\in\mathbb{N}}$ in ...