# Tagged Questions

This tag is used if a reference is needed in a paper or textbook on a specific result.

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### Text for studying group representations in the context of (abstract) harmonic analysis

I would like to study elements of representation theory as I often encounter it when reading texts on harmonic analysis. I was therefore curious if someone could recommend a book for this. When ...
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### Points of continuity of a lower semicontinuous function have non empty interior

Let $X\subset \mathbb R^d$ having non empty interior and let $f:X\to\mathbb{R}$ be lower semicontinuous. I know that the set of discontinuities of such a function is contained in a meager set, and ...
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### Smooth dependence on the initial condition of the integral of an ODE

I am considering an ODE $\dot{x}=f(x)$, with $x\in\mathbb{R}^d$ and $d<\infty$. $f$ is a $C^k$ function and I denote by $\Phi_t x$ be the value of the solution at time $t$. I assume that my ODE ...
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### Can infinitely many orbifolds be “added up” to form a fractal space?

Disclaimer: this question is rather vague and thus might not be suitable for this site. If so, feel free to tell me and I'll delete it. Intuitively, an orbifold, from what I understand, is a "...
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### What is the extension of the truth-table degrees to Baire Space called?

Recall that for sets $A, B \in 2^\omega$ that we say $A \leq_{tt} B$ if there is a total Turing functional $F \colon 2^\omega \to 2^\omega$ such that $F(B)=A$. This is called truth-table reducibility....
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### Maximal subgroups of $\mathrm{SL}(n,\mathbb{R})$

I would like to find a list (or at least a description) of the maximal closed connected subgroups of $\mathrm{SL}(n, \mathbb{R})$ , and also of $\mathrm{SU}(p,q)$. In the following MO discussion is ...
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### Expository articles on Algebraic Number Theory

I am about to start learning Algebraic Number Theory and thus was looking for some expository articles on this subject. So far I have found two such articles: Dickson, L. E.. (1917). Fermat's Last ...
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### Thorough reference on regular homotopy

I would like to learn this topic of algebraic topology but I cannot find a relevant reference to answer my basic questions on the subject (for example, is there a Hurewicz theorem for regular homotopy ...
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### Dual equivalence for multioperators

This is a reference request question. But let's start with a few definitions. Let $L$ and $M$ be two bounded lattices. A multioperator $p$ for $L$ and $M$ is an application $$p : L \to Ft(M)^{op}$$ ...
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### Regarding a conjecture Fogarty proposed

In a paper by Fogarty titled "Algebraic Family On An Algebraic Surface," he conjectured that $\bf Hilb^n(\mathbb P^N)$ is always variety-- reduced and irreducible. Is this still a conjecture; any ...
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Let $(M, g)$ be a compact Riemannian manifold, and let $\lambda^2$, $\varphi_\lambda$ represent eigenvalues and eigenfunctions respectively of the Laplacian $\Delta$, that is, $-\Delta \varphi_\lambda ... 0answers 43 views ### The integral of$\Gamma\left(\zeta\right) \, W_{-\zeta,\mu}(z) $Someone has a reference that addresses an integral of the followns type $$I_{a,b,x} = \int_{0}^{+\infty} \zeta^{-a} \, \Gamma\left(\zeta+b\right) \, W_{-\zeta-b,\tfrac{-1}{2}}(x) \, d\zeta$$ where ... 2answers 234 views ### Attaching an ideal whose square is zero: does this operation have a name and a notation? I know I met the following construction somewhere, but I cannot remember where. Let$A$be a (unital associative) ring, and let$N$be an$A$-$A$bimodule. On the product set$A\times N$we define ... 0answers 124 views ### Categories where every Mono Splits When every epi splits a category is said to satisfy the Axiom of Choice. When every idempotent splits a category is called Cauchy Complete or Idempotent complete. These look to be well-studied ... 1answer 141 views ### Want more details about the image of a Maass form in the AIM press release concerning LMFDB Actually I came upon this through MO a couple of days ago: in here (http://aimath.org/aimnews/lmfdb/) there is a mesmerizing image The caption reads A Maass form, one of the 20 different types ... 0answers 159 views ### Where can I find Andre's “Cinq exposés sur la désingularisation”? Many expositions of Popescu's desingularization theorem indicate that an other proof of this theorem can be found in "Cinq exposés sur la désingularisation" by M. Andre, Ecole Polytechnique ... 2answers 130 views ### base point in Heegaard Floer homology It is stated in Mcduff's overview paper "FLOER THEORY AND LOW DIMENSIONAL TOPOLOGY", end of page 9, that the Heegaard Floer homology without considering a base point depends only on the homology of ... 2answers 266 views ### Surfaces contained in a ball In this Paper there is a proof that a closed plane curve of length$L$and curvature bounded by$K$can be contained inside a circle of radius$L/4 - (\pi - 2)/2K$. Are there similar results for ... 1answer 336 views ### Combinatorics problem about sum of natural numbers Following combinatorics problem is claimed to be an open problem in "The Princeton Companion to Mathematics" (pp. 6) Let$a_1,a_2,a_3,...$be a sequence of positive integers, and suppose that each ... 0answers 99 views ### What to do about Secondary Results that are of Independent Interest? I am thinking about writing an online article about a simplified algorithm for a problem$P$, for which efficient solutions are already known, whose implementation is however challenging. My ... 0answers 128 views ### Reference for the Hodge polynomial or the Hodge Characteristic What is the first work that studies, refers to, or mentions the Hodge characteristic? The Hodge polynomial is the unique ring homomorphism$$P_{hdg}:K_0(\mathbf{Var}/\mathbb{C)}\to \mathbb{Z}[u,v,u^{... 1answer 98 views ### Pfaffian of several skew-linear transformations / matrices Introduction: Let's assume we have a 2-form$\alpha=(1/2)\sum_{j,k=1}^n a_{jk}\ e_j\wedge e_k$, where$n=2m$, and$a_{jk}\in\mathbb C$. We know that$\alpha^{\wedge m}=\alpha\wedge\alpha\dots\wedge\...
If $X$ is a closed $n$-manifold, a fake $X$ is another closed manifold homotopy equivalent to $X$. There is some interest in classifying manifolds (up to, say, homeomorphism) homotopy equivalent to a ...