# All Questions

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### Is stable map space $\overline{M_{0,n}}(\mathbb{P}^n,d)$ is irreducible for all n,d?

I read a paper 'Notes On Stable Maps And Quantum Cohomology, W.Fulton and R.Pandharipande'. And I think that $\overline{M_{0,n}}(\mathbb{P}^n,d)$ is irreducible. But I cannot find an exact statement ...
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### Structure of $C^k$ ($k<\infty$)Riemannian metrics on a manifold

$M$ is a smooth manifold. It's known that if $M$ is compact, then the space of smooth Riemannian metrics has a Frechet manifold structure. For the space of $C^k$($k<\infty$) Riemannian metrics, ...
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### realizing uniform boundedness of Galois representations associated to elliptic curves

This is less of a question and more of an argument that I've been worried about for a while and want to check (apologies for the length and if my writing is unclear). Suppose I have an elliptic curve ...
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### Weighted maximal number of disjoint chains in the integer divisibility poset for $\{1,2,\ldots,n\}$

In the mathoverflow question here the asymptotic growth of antichains in the divisibility poset ${\cal P}_n$ of the set of natural numbers $\{1,\ldots,n\}$ is considered. I have a somewhat dual ...
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### Are there $n$ groups of order $n$ for some $n>1$?

Denote $N(n)$ : number of groups of order $n$ Does $N(n)=n$ hold for some $n>1$ ? I checked the OEIS-sequence https://oeis.org/A000001 as well as the squarefree numbers in the range ...
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### Curve with Matlab [on hold]

I have posted this question: http://math.stackexchange.com/questions/1547373/curve-with-matlab but I have not answers. Can you help me?
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### non commutative polynomial which is zero for all matrix evaluation

I want to work on $K$ an algebraic closed (commutative) field of characteristic zero (even if it seems to be more general). We can define the free K-algebra of polynomials in non commutative ...
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### An inequality improvement on AMM 11145

I have asked the same question in math.stackexchange, I am reposting it here, looking for answers: How to show that for $a_1,a_2,\cdots,a_n >0$ real numbers and for $n \ge 3$: ...
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### Traces of fractional Sobolev spaces $W^{s,p}$ with $0<s<1/p$

I've stumbled upon a problem involving the trace of a function in a fractional Sobolev space of the form $W^{s,2}(H)$, where $H$ is a half-plane in $\mathbb{R}^2$. Would it be possible to define a ...
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### Wreath product of an abelian group with a nilpotent group

By work of Coulbois, the wreath product of two finitely generated free abelian group is $LERF$; i.e, every finitely generated group of this wreath product is closed in the profinite topology. Is there ...
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### Compact factors of Lie groups; possibly varying definitions [migrated]

Let $G$ be a real connected semisimple Lie group. Are the following equivalent?: (1) $G$ has no proper cocompact Normal subgroups. (2) $G$ has no proper cocompact connected Normal subgroups. In ...
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### Inequality for the maximum of Gaussian variables

Let $X=(X_1,\dots,X_n)$ and $Y=(Y_1,\dots,Y_n)$ be centered Gaussian vectors with variance matrix $\Gamma_X$ and $\Gamma_Y$. We assume that the matrix $\Gamma_Y-\Gamma_X$ is positive definite. Is it ...
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### Is the positive existential theory undecidable?

Could you tell if the positive existential theory of $\mathbb{C}[e^{\mu x} \mid \mu \in \mathbb{C}]$ is undecidable in the language $\{+, \cdot , \frac{d}{dx} , 0, 1, e^x\}$ ? How can we prove the ...
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### If $k$ is an algebraically closed field of any characteristic, then the fundamental group of $A$ is abelian

This is a followup to my earlier question, see here. I reproduce it as follows. Let $A$ be an abelian variety over a field $k$ of characteristic $0$. How do I prove, without using transcendental ...
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### Simplicial approximation diagram [on hold]

Let $K$ and $L$ be simplicial complexes as given, and let $\phi:|K|\to|L|$ be the continuous map, where $A=\phi(a)$, $B=\phi(b)$, and so on. Check whether the map $\phi$ has a simplicial ...
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### all subsets borel

Assume Martin's axiom plus $\neg CH$. It is well known, via almost disjoint forcing, that every set of reals of size less than continuum is an example of a metric space whose subsets are all ...
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### F-points of product of closed subgroups vs. product of F-points, F a local field, reference?

Let $F$ be a finite extension of $\mathbb Q_p$, where p is an odd prime. Let $G$ be a connected reductive group defined over $F$. Let $M, H$ be closed $F$-subgroups of $G$ (in particular, I'm ...
Given two probability distributions $p,q$ on a finite set $X$, the quantity variously known as relative information, relative entropy, information gain or Kullback–Leibler divergence is defined ...