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Equivariant isometric embedding of manifolds in a Hilbert space under a noncompact group action

Given a Riemannian manifold $M$ and a group of isometries $G$ of $M$, I am interested in when there exists a isometric embedding $\iota : M \to H$, where $H$ is a Hilbert space and a representation ...
1answer
111 views

Closeness graph of a topological space

Let $(X,\tau)$ be a topological space. We say that $x, y \in X$ are close if for every neighborhood $U$ of $x$ and $V$ of $y$ we have $U\cap V \neq \emptyset$. Let $E$ be the set of $\{x,y\}$ where ...
0answers
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Constructing an additive set function from on a non-additive one

repost from math.se. I was trying to generalize some results from measure theory to functions that are "almost" measures but not additive. Then, I thought it could be interesting to do this in a ...
0answers
33 views

If the total number of divisors of the square of a number is 7 less than the number, what is the total number of divisors of cube of that number [on hold]

if the total number of divisors of the square of a natural number N is 7 less than N, then what is the total number of divisors of cube of N
3answers
74 views

0answers
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What is the etale sheafification of the (unramified) Milnor-Witt $K$-theory

I would like a reference/argument for the truth/falsity of the following statement: The etale sheafification of the unramified Milnor-Witt K-theory (Nisnevich) sheaves are the (etale sheafification ...
0answers
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Let $f_{c}:Z_2^n \rightarrow \{-1,1\}$ be the character defined as $f_c(x) = (-1)^{<x,c>}$, where $c,x \in Z_2^n$. It is easy to see that since $f_{c_1}\cdot\ldots\cdot f_{c_k} = f_{c_1 \oplus ... 12answers 3k views Essays and thoughts on mathematics Many distinguished mathematicians, at some point of their career, collected their thoughts on mathematics (its aesthetic, purposes, methods, etc.) and on the work of a mathematician in written ... 0answers 44 views Factorial Sums over Compositions or Unlabeled Permutations" Let$C_n$denote subset of integer compositions of$n$and$c=(c_1,c_2,\dots c_n)$In a divergent sum, the sequence $$a_n=\sum_{c\in C_n} \prod_{c_i\in c} c_i!$$ frequently shows up and one ... 0answers 31 views Systems of linear modular equations with unknowns in the moduli I am interested in systems of linear modular equations, where the unknowns also appear in the moduli. The general form would be:$A \vec{x}= \vec{b} \;\textrm{mod} \; (C \vec{x}+\vec{d})$where A ... 0answers 21 views References on Lorentzian geometry with non-vanishing torsion [on hold] For my thesis I have to study Lorentzian geometry with non-vanishing torsion. Do you know any references on this? 'Riemannian geometry' with non-vanishing torsion will also be usefull. 0answers 44 views What are eigenbasis of binary brownian motion? [on hold] I am seeking for a closed-form expression of eigenbasis for binary brownian motion sign(cumsum(randn(n,1))). Eventually, I need an associate fast transform for this ... 2answers 132 views Differential structures and K-homology groups What is an example of a (compact) manifold, which has two non-equivalent differential structures such that the K-homology groups are non-isomorphic? If no such example exists, i.e. "K-homology does ... 0answers 143 views Formal generic fibre and Fermat's Last Theorem Set$A_{n} \colon= {\Bbb F}_p[[S_1,...,S_n]]$and$A_{n,d} \colon= {\Bbb F}_p[[S_1,...,S_n]][[X_1,...,X_d]]$be a$d$-variables formal power series ring over$A_n$. We denote by$K$the fractional ... 0answers 41 views Singularities of the Quantum propagator (baby version) Given$a,b \in \mathfrak{su}(4)$which are taken to generate the whole algebra, consider the following map$V:\mathbb{R}^{2} \rightarrow SU(4)$:$V : (w_1, w_{2}) \mapsto e^{(a+w_2 b)} e^{(a+w_1 b)}\$ ...

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