# Tagged Questions

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### Finding generalised Lyndon words

Let $\Sigma = \lbrace a_1, \ldots, a_n, A_1, \ldots A_n \rbrace$ (where $A_i = a_i^{-1}$) and $\prec$ be a total ordering on $\Sigma$. Let $\Sigma^*$ be the set of all words (generated by the ...
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### Is the limit set of a group action always closed?

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 ...
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### “Spectral decomposition” action on the unitary group

Consider a matrix $U$ from the unitary group $U_N(\mathbb{C})$ and consider the map $f:U_N(\mathbb{C})\rightarrow U_N(\mathbb{C})$ where $f(U)$ is the matrix of the eigenvectors of $U$. What is ...
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### Minimality of time-t minimal flows

This question is mainly motivated by the question Transitivity of a flow and its time-1 map Let $M$ be a closed smooth manifold and $\Phi\colon\mathbb{R}\times M\to M$ be a smooth minimal flow, i.e. ...
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### A possible generalization of the Borsuk Ulam theorem via action of symmetric groups

The symmetric group $S_{m}$ is equiped with the counting Har measure $\mu$ and the obvious sgn character. Assume that $S_{m}$ acts on $S^{n}$, $n\geq m-1$ and $f:S^{n}\to \mathbb{R}^{n}$ ...
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### 2 questions on Nagata's counterexample; $k[f_1,…,f_r]=k[g_1,…,g_s]$ vs. $k(f_1,…,f_r)=k(g_1,…,g_s)$

Let $\{a_{ij}\}$ for $i=1,2,3$, and $j=1,...,16$ be algebraically independent elements over some prime field. Let $k$ be a field containing all $a_{ij}$. Then consider $k^{16}$ as $k$-vector space and ...
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### Faithful actions of finite groups on topological spaces

Suppose that $G$ is a finite group acting faithfully on a topological space $X$. In the smooth setting, one can deduce that for each $x$ in $M$, the induced map $$G_x \to Diff_x\left(M\right)$$ from ...
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### Certain principal bundle structure on $\mathbb{R}^{n} \setminus \{0\}$

I ask this question in MSE and I received no answer, so I repeat it here: Is there a right action of $\mathbb{H}^{2}$ on some $\mathbb{R}^{n}\setminus \{0\}$ such that this action gives us a ...
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### Name for condition on map of cancellative monoids

Let $M,N$ be cancellative monoids with identity $\epsilon$ and suppose that $k\colon M\rightarrow N$ is a function such that $k(\epsilon)=\epsilon$ for all $a,b\in M$, there exists $v\in N$ such ...
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In order to calculate Tamagawa numbers, I need to justify that for a nice (say Schwartz-Bruhat) function, the following identity holds : $$\int_{\mathbf{A}^2} f(x)dx = \int_{SL_2(\mathbf{A})/SL_2(K)} ... 0answers 71 views ### Invariant subsets of a local action I have also asked this in MSE, but it seems to me that my question wasn't very well received there and I think someone in here will be able to answer it more quickly, hence this post. I don't ... 0answers 189 views ### Rational conjugation of elements of a finite group Let G be a finite group. Two elements x and y of G are said to be rationally conjugate, written x \sim_{r} y, if and only if \langle x\rangle and \langle y\rangle are conjugate subgroups ... 0answers 125 views ### Actions and representations of profinite groups Let p be a prime number, and denote by \mathbb{Z}_p the additive profinite group of p-adic integers. Let G be a finitely generated profinite group of order coprime to p, and V = \mathbb{Z}_p^{... 0answers 146 views ### When a Whitney stratification has no stratum of codimension one? Let G be a compact Lie group, and M be a smooth n-dimensional G-manifold which admits an orientation preserving the G-action. Then M has a natural Whitney stratification induced by the ... 0answers 89 views ### Smoothing of a hyperquotient singularity Let f be a polynomial in k complex variables, and suppose the affine variety V given by f = 0 has an isolated singularity at the origin, but is otherwise smooth. Now assume that some cyclic ... 0answers 90 views ### invariant lines avoiding fixed subvarieties Could anybody help me with the following question ? Assume we are given: (1) a finite order (linear) automorphism g of the complex projective space \mathbb{P}^r, (2) a closed algebraic ... 0answers 515 views ### Questions on orbit properties of group action on varieties Let F be a p-adic field or \mathbb{R},\mathbb{C}, G a group(not necessarily reductive) over F, X an algebraic variety defined over F, and G acts on X. Now we have several questions ... 0answers 66 views ### On orders of stabilisers of group actions and stacks Let X be a finite type irreducible separated DM-stack over \mathbb C. Let x be an object of X(\mathbb C) with stabilizer G_x. Let y be an object of X(\mathbb C) with stabilizer G_y. ... 0answers 58 views ### Submanifolds invariant under subgroups with identical quotients given a smooth manifold M^n and a finite group G acting smoothly and effectively, let's consider two (embedded) k-dimensional submanifolds N_1,N_2\subset M and two subgroups H_1,H_2\subset G ... 0answers 115 views ### Action of semidirect products of cyclic groups Is there anything known about group actions of C_{p}\rtimes C_{p}^{*} on the ring of real polynomials \mathbb{R}[X_{1},\ldots,X_{n}], where C_{p} denotes the cyclic group of order p and p is ... 0answers 75 views ### Stable analytic manifold under simple action For an integer m > 1, let us define the action$$ f: X_i \to (1+X_i)^{m} - 1  on $C[[X_1,...,X_N]]$, where $C$ is the complex number field. Consider the analytic manifold $V(I)$ defined by the ...
Let $X$ be a nice algebraic variety (say smooth, projective) over a field of characteristic 0. Let $G$ be an abelian group acting on $X$. For each subgroup $H$ of $G$, denote by $X^H$ the closed ...
Let $C_n$ be the cyclic group of order $n$ acting on a finite set $X$ and let $Z(C_n, X; p_1,p_2,\dots)$ be the cycle index of the corresponding permutation group. I wonder whether the knowledge of ...