This tag is used if a reference is needed in a paper or textbook on a specific result.
0
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14 views
Reference Help: Matsuki duality Orbits
I'm studying the Matsuki duality of $G_0$-orbits and $K$-orbits over a flag manifold $G/P$ where $G$ is semisimple complex Lie group and $P$ is a parabolic subgroup. I would like to study some ...
1
vote
1answer
40 views
Strictly contracting elements in the center of a Levi subgroup
Let $G$ be a connected reductive group over a non archimedean local field $k$.
Let $P \subset G$ be a parabolic subgroup with Levi decomposition $P=MN$, $Z_M \subset L$ be the center of $M$ and $S_M ...
0
votes
0answers
49 views
Sources in unimodular rows
I'm beginning to study more advanced material of module theory and I need to study more about unimodular rows. I would like a good introductory book or pdf speaking about unimodular rows with ...
8
votes
1answer
177 views
Explicit isomorphism for quaternion algebras over $\mathbb{Q}$?
It is known that the isomorphism class of a quaternion algebra $A=\binom{a,b}{K}$ over a number field $K$ is determined by the finite set of places $v$ of $K$ where $A\otimes_K K_v$ is a division ...
2
votes
1answer
128 views
Name and references for a “twisted” addition in a ring
This question may seem a little unmotivated, but it actually isn't something that just occurred to me out of nowhere. It stems from a discussion I had the other day with a friend and is directly ...
5
votes
2answers
149 views
Genus of Tutte-Coxeter Graph
What is the genus of the Tutte-Coxeter graph -- the incidence graph of the
GQ of order 2? Seems like it should be well known, since nearly every other
parameter for that graph is known, but I can ...
5
votes
0answers
108 views
Is there a holomorphic Morse-Bott lemma?
It asks for a generalization of the question in the post
Normal form for a holomorphic Morse function
Suppose $f$ is a holomorphic function on a complex manifold $M$ which has Bott type critical ...
6
votes
0answers
106 views
Phillips-Sarnak conjecture in higher dimension
The Phillips-Sarnak conjecture states that for a generic Fuchsian lattice the space of Maass cusp forms is finite-dimensional. Generic here means in particular non-uniform, non-arithmetic, no special ...
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0answers
130 views
An extrasensory perception strategy :-)
I asked this question at MSE some months ago
but I received only partial answers, so I put it here. The following sounds nice for me and I spent a good time during the investigation. But I am a ...
-1
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0answers
65 views
Reference on Infinite Dimensional Manifold [migrated]
I am studying manifold. For comprehension, I read the site http://en.wikipedia.org/wiki/Manifold, and there is some information about infinite dimensional manifold.
Now I have two questions or ...
3
votes
0answers
157 views
Looking for Soviet Math. Dokl
I'm a undergraduate student and I'm trying to study research level papers for the first time. I'm studying William Weiss's "Countably compact spaces and Martin's axiom" and he gives "Soviet Math. ...
10
votes
2answers
367 views
Postnikov's algebraic reconstruction of cohomology from homotopy invariants
In his short paper (1951) and longer monograph (1955), Postnikov introduced what I believe are now called Postnikov systems or towers. It is my understanding that Postnikov systems have since then ...
5
votes
2answers
198 views
Formal completion of the normal bundle
Let me for simplicity start with affine case. If $X=\operatorname{Spec}(A)$ is an affine variety $Z \subset X$ is a closed affine subvariety $Z=\operatorname{Spec}(A/I)$. What conditions are ...
0
votes
1answer
78 views
Characterizing Inf and Sup sets
Suppose $X$ is a set. Let $\Xi$ be the set of all pairs $(\mathcal A,\mathcal B)$ such that
$$\mathcal A, \mathcal B \subseteq \mathcal P(X)$$
and for some partial order $\le$ on $X$, $\mathcal A$ is ...
6
votes
3answers
445 views
Consistency of Analysis (second order arithmetic)
Is there a proof of the consistency of Analysis (second order arithmetic), which is similar to Gentzen's proof of the consistency of arithmetic?
Update:
Which (different) methods can be used to ...
1
vote
0answers
60 views
unique types and decidability
Suppose $\mathcal{M}$ is an infinite structure which has the property that every type that is realised is realised uniquely. Also assume that every element of $\mathcal{M}$ is definable but there is ...
3
votes
1answer
168 views
Colorful model theory
There are a number of concepts in model theory - often situated around Hrushovski's amalgamation method (see for instance http://math.univ-lyon1.fr/~wagner/nijmegen.pdf) - which are colorfully named:
...
2
votes
0answers
38 views
What do we know about the generlized eigenvalue problem involving a projector?
Consider a matrix $A\in\mathbb{R}^{n\times n}$ and a projector $P\in\mathbb{R}^{n\times n}$.
Are there results regarding the generalized eigenpairs $(v,\lambda)$ of the generalized eigenproblem
...
4
votes
1answer
166 views
Perfect set property implies $\omega_1$ is a limit cardinal in $L$
Specker proved in 1957 that if in $V$ every set of real numbers has the perfect set property, than in $L$, $\omega_1^V$ is actually a limit cardinal.
The original proof is in German, and I've been ...
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votes
2answers
91 views
Poincaré bundle and Weil pairing for Abelian schemes
In which situations is there a Poincaré bundle for Abelian schemes? In [Mumford, Abelian varieties] only the case of Abelian varieties is treated.
The same question for the Weil pairing ...
0
votes
0answers
17 views
Equivalence of Lp harmonic functions on the ball and a representation by harmonic homogeneous polynomials
In Harmonic function theory there is a theorem which say if $u$ is a harmonic function on $B\left(a,r\right)$, then there exist homogeneous harmonic polynomials $p_{m}$ in $\mathbb{R}^{n}$ such that ...
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votes
0answers
177 views
A Bundle associated to a submanifold of $\mathbb{R}^{n}-\{0\}$
Edit:
According to the comment of Rayan Budney I revised the question as follows:
Let $M$ be a submanifold of $\mathbb{R}^{n}-\{0\}$. We define a $n-1$ dimensional bundle
\begin{equation}
...
3
votes
1answer
224 views
Does there exist a function such that $\int_{\mathbb{R}_+^{\star} } t^nf(t)dt=0$? [on hold]
Let $f\in C([a,b],\mathbb{R})$ such that $\displaystyle\int_{a}^{b} t^nf(t)dt=0$ for all integer n.
We know that $f\equiv 0$. It's call Hausdorff theorem.
This theorem is wrong on $\mathbb{R^+}$, a ...
0
votes
0answers
21 views
A solution of the heat equation with Robin boundary condition on a closed interval [migrated]
Suppose $I$ is an interval $[a, b]$. $u(t,x)$ satisfies the following heat equation:
$$ \frac{\partial}{\partial t} u(t,x) =\frac{\partial^{2}}{\partial x^{2}} u(t,x) $$
with boundary condition
$ ...
4
votes
0answers
48 views
Reference for statement that almost every $n$-element partial order has trivial automorphism group
I'm looking for a reference for the statement that almost every partial order on $n$ elements has trivial automorphism group. I've been told that this is a folklore result. Does anyone know of a ...
7
votes
2answers
197 views
Cokernel of the stable J-homomorphism at odd primes
Where can one learn about odd-primary components of the cokernel of the stable J-homomorphism?
According to wonderful Wikipedia article on Homotopy groups of spheres, the "hard" part of the stable ...
5
votes
0answers
52 views
K-Theory and completion [duplicate]
I vaguely remember the existence of a statement that relates the $K$-theory (in the sense of Quillen) of a noetherian local ring $A$ with maximal ideal $\mathfrak{m}$ with the $K$-theory of the ...
5
votes
0answers
62 views
Classifying two-faces of four-polytopes
Motivation: This question is related to my study of hyperbolic Coxeter polytopes. In general, if one put some restrictions on the type of their dihedral angles (say, all dihedral angles are equal to ...
1
vote
0answers
80 views
Euler class and self-intersection number of a surface in a 4-manifold [duplicate]
In the first two paragraphs of Circle bundles over $CP^1$ and self-intersection number of $CP^1$ embeddings, it is claimed that
For a compact oriented surface $X$ in a 4-dimensional oriented ...
6
votes
1answer
157 views
Renewal systems: Intrinsic ergodicity and a question related to the Adler's conjecture
Consider the alphabet $\mathcal{A} = \{0,1\}$ and consider a finite set of words $W = \{\omega_1, \ldots , \omega_n\}$ over $\mathcal{A}$. Then the renewal system $\Sigma_{W}$ generated by $W$ is ...
5
votes
1answer
89 views
Properties of singularities that are preserved by categorical quotients
Let $G$ be a reductive group acting on an affine singular
variety $X$, and let $X/G$ be the categorical quotient. I know that if
$X$ has rational singularities, then so does $X/G$ ...
4
votes
1answer
136 views
Which hyperbolic tilings are Cayley graphs?
I realise the question is easy but after asking to a few people (and never getting a clear answer), I thought it could be instructive to ask it here:
Given a regular tiling of the hyperbolic plane is ...
3
votes
1answer
210 views
Flow of an integer
I've stumbled across this family of flow networks, and posted the sequence of maximal flows to OEIS. It doesn't appear at this time. I can't find any reference to it either. Has anyone seen it?
...
1
vote
1answer
50 views
reference request: Riesz/Newton potential and HLS inequality in L1.logL1
Let's consider in dimension $d\geq 3$ the Newton/riesz potential $f=I_2[g]$
$$
f(x)=\int_{R^d}\frac{1}{|x-y|^{d-2}}g(y)dy,
$$
which solves $-\Delta f=g$ (up to positive normalizing constants, which I ...
11
votes
0answers
130 views
Entropy in elimination theory, or a brief remark by Gelfand-Kapranov-Zelevinsky
In the introduction to their book "Discriminants, resultants and multidimensional determinant", the authors state a very intriguing observation concerning the coefficients of monomials appearing in ...
2
votes
1answer
85 views
Pullback of $L^p$ functions via exponential map
Let $M$ be a complete Riemannian manifold, endowed with its exponential map $\exp: TM \longrightarrow M$. For any $C^k$- function $u$, we get the Pullback
$$ \exp^* u = u \circ \exp$$
which is in ...
16
votes
3answers
2k views
Silly me & Van der Waerden conjecture
So I walked into this very innocent-looking combinatorics problem,
and quite soon I ended up with the problem to prove that any doubly stochastic $n \times n$ matrix has a non-zero permanent.
Now ...
3
votes
2answers
399 views
An identity in an arbitrary commutative ring
This fact might be either trivial, wrong, or well known.
Let $R$ be a commutative ring. Let $u_1,\dots,u_{s-1},u_s\in R$ and $m,M\in R$. Let us assume that $m,M$ satisfy
$$(m-u_1) \dots ...
2
votes
1answer
180 views
Forcing Notions with Unknown Real/Cardinal Preserving Situations
Question. Is there any set forcing notion $\mathbb{P}$ in one of the following categories?
(a) $\mathbb{P}$ preserves cardinals but it is still open whether $\mathbb{P}$ adds reals or not.
(b) ...
2
votes
1answer
61 views
Extendability of $L^{p}$ harmonic functions
Let $u$ be a harmonic function on some open set $\Omega\subset\mathbb{R}^{n}$ and $u\in L^{p}\left(\Omega\right)$. Is there any reference on extending $u$ to harmonic function on a larger open set ...
4
votes
1answer
173 views
Is Van der Waerden's function elementary
Van der Waerden's function was proved to have elementary upper bound on growth rate.
Is the Van der Waerden's function itself elementary in the sense of Kalmar?
3
votes
1answer
150 views
Higher dimensional analogue of Thue's equation
The classical Thue equation is
$$\displaystyle F(x,y) = h,$$
for a binary form $F(x,y) \in \mathbb{Z}[x,y]$. Recall that a binary form is a polynomial in two variables which is homogeneous, and $h$ ...
3
votes
1answer
89 views
The spectral radius of a modified graph
Let $H$ be a graph and let $G=H \vee K_{1}$ be obtained by creating a new vertex and joining it to every vertex in $H$.
This situation has many different names: $G$ is called the cone or the ...
5
votes
3answers
189 views
A weak-mixing, zero entropy measure on the 2-shift which gives equal weight to both symbols
I am currently sketching a paper in the general area of symbolic dynamics in which I would like to be able to use the following fact:
Proposition (proposed): there exists a shift-invariant ...
3
votes
1answer
102 views
Reference to definition of matrix log with domain SO(3) which is Borel measurable
I was trying to set up an inverse to matrix exponential $\exp:\mathrm{Skew}(3\times 3)\to SO(3)$ that "covers" the biggest possible domain and is Borel measurable. I was wondering if there is a ...
8
votes
0answers
129 views
Obtaining a lightface pointclass from a boldface one
Define a pointclass to be:
boldface inductive-like if it is $\mathbb{R}$-parameterized, has the scale property, and is closed under $\wedge$, $\vee$, $\forall^\mathbb{R}$, $\exists^\mathbb{R}$, and ...
5
votes
0answers
177 views
1-Wasserstein distance between two multivariate normal
The $p$-Wasserstein between two measures $\nu_1$ and $\nu_2$ on $X$ is given by
...
1
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0answers
55 views
Is there any study on limit sets arising from “outside” of the hyperbolic geometry?
In the projective model, hyperbolic spaces are modeled by the interior of the light cone of Lorentz spaces. Kleinian groups are isometries of the hyperbolic space, and they centainly also act on the ...
1
vote
1answer
70 views
L logL space and compactness
I think that if a sequence of L^1 functions have the integral
$$
\int f_n \log (f_n)dx
$$
uniformly bounded, then there is a subsequence that converges strongly in $L^1$.
The questions are:
1) Is ...
3
votes
0answers
65 views
Question about a length inequality in algebraic dynamics
Let $X$ be a Noetherian scheme. Let $f\colon X\rightarrow X$ be an integral self-morphism. If $x\in X$ is a closed point, I will write $\mathcal{F}_{1}^x$ for the coherent sheaf of ...
