# All Questions

**0**

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8 views

### Map between homotopy groups of O, related to J-homomorphism and K-theory of Z

Let $s \geq 0$ be fixed. The $J$-homomorphism includes $\pi_{8s+1}(SO) = \mathbb Z/2$ in $\pi_{8s+1}^s$, the $(8s+1)$-th stable homotopy group of spheres.
Now regard $\pi_{8s+1}^s = \pi_{8s+1} ...

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2 views

### Examples of non-extremal subfactors

Every subfactor $(N \subset M)$ in this post are supposed to be finite index inclusion of ${\rm II}_1$ factors.
Definition (here p64): Such a subfactor is called extremal if $tr_{N'} = tr_M$ on ...

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11 views

### finite generation of a certain type of subring

Let $k$ be a field, and let $R$ be a finitely generated $k$-algebra. (If it helps, you may assume $R$ is an integral domain.) Let $I$ be an ideal of finite colength. Note that $A:=k+I$ is a subring ...

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11 views

### Which properties determine the uniqueness of the local Artin map?

Any abelian extension of local fields can be realized as the completion of a global abelian extension. So let $L/K$ be abelian, $w/v$ an extension of places. From the global Artin map on ideles we ...

**9**

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81 views

### What can topological modular forms do for number theory?

Topological modular forms ($TMF$) have in the recent years made an impact in algebraic topology. Roughly, the spectrum $tmf$ is the (derived) global sections of the sheaf of $E_\infty$ ring spectra ...

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9 views

### Suggestions for dealing with the “timed” balls-into-bins model

Definitions: Let $T$ (for "time") be a random variable $T \sim \text{Exp}(\lambda)$ and $\Delta t$ is a realization (or called an observed value) of $T$. Let $D$ (for "delay") be a random variable $D ...

**-7**

votes

**1**answer

64 views

### IMPA (Brazil) vs Iowa State University (USA) [on hold]

I was recently offered admission to Iowa State for a math PhD.
I thought they were to deny me admission since they had not answer me until now (I spected an answer in March). Since I had not had a ...

**-1**

votes

**0**answers

13 views

### associated prime of a module under a ring homomorphism

Let $f: A\rightarrow B$ be a homomorphism of Noetherian rings, and $M$ a $B$-module(not necessarily finitely generated).
Question: Is $^af(Ass_B(M))=Ass_A(M)$?
If $q$ is an associated prime of the ...

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votes

**0**answers

26 views

### Prove the isomorphism of categories $Fun(\mathcal{A}\times\mathcal{B},\mathcal{C})\cong Fun(\mathcal{A},Fun(\mathcal{B},\mathcal{C})),$ [migrated]

I'm a computational engineer starting with a course of Introduction to Category Theory, and perhaps is extremely basic what I'm asking but I'm trying to learn how to make proofs in category theory ...

**1**

vote

**1**answer

53 views

### Acyclic complexes for extraordinary cohomology theories

Let $X$ be a CW complex such that for all extraordinary homology theories, if you plug $X$ into them you get the same value as plugging in a point. Must $X$ be contractible?

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23 views

### When can two Cauchy transforms intersect?

Given two polynomials $p$ and $q$ over reals and being guaranteed that both have all roots real I want to know if there is any characterization of the solutions of the equation $\frac{p'}{p} = ...

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46 views

### Hyperplane sections of algebraic groups

Let $P_i$ denote the $i-th$ vertex in the Dynkin diagramm of an algebraic group. It symbolizes a parabolic subgroup of $G$ corresponding to the other vertices, meaning $G/P_i$ is a smooth, projective, ...

**1**

vote

**1**answer

136 views

### How does the solenoid structure of $\mathbb{A}/\mathbb{Q}$ lift to $PGL(2, \mathbb{A})/ PGL(2, \mathbb{Q})$?

Some papers I am reading talk about an "adelic" object $PGL(2, \mathbb{Q}) \backslash PGL(2, \mathbb{A})$ . This has sparked a lot of confusion since I don't know what such a quotient could mean.
A ...

**4**

votes

**1**answer

40 views

### Penrose tiling substitution is bijective

Let $\mathcal{P}$ a Penrose tiling built by a substitution $\omega$ with two triangles.
It is claimed, for instance, in the article of Anderson and Putnam "Topological invariants for substitution ...

**0**

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**0**answers

75 views

### Soft Question: Relationships Between Moduli Space and Objects They Parametrize

Apologies in advance if this question is not suitable for MO. My friend and I were wondering recently what, if any, are the relationships between the geometric properties of a moduli space and the ...

**1**

vote

**0**answers

8 views

### Dual cone of 'positive' Bochner integrable functions

If we consider the space of integrable functions $L^1([0,1];\mathbb{R})$, it can be ordered by the convex cone of positive integrable functions $L^1([0,1];\mathbb{R}_+)$. It is known that the ...

**0**

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20 views

### Quantum dimension in SU(N) level k Kac-Moody algebra

The CFT of the SU(N) level k Kac-Moody current algebra has many Kac-Moody primary fields. I wonder if any one has calculated the quantum dimensions of those Kac-Moody primary fields.
I know that, ...

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**0**answers

23 views

### Singularities of the product of a $(\mathbb{C}^*)$-surface with $\mathbb{C}$

Recall that any normal $\mathbb{C}^*$-surface is Cohen-Macaulay
and there exists normal $\mathbb{C}^*$-surfaces whose
singularities are not rational.
Does anyone know an example of a normal ...

**1**

vote

**1**answer

118 views

### Ask the name of a combinatorial theorem

It is a classical theorem. For given integer $n \ge 1$, among ${n\choose{n/2}} = 2^{(1-o(1)n)}$ strings in the cube $\{0, 1\}^n$ with weights $n/2$, i.e., $n/2$ indices are 1, there are at least ...

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**0**answers

32 views

### Schubert Polynomials for Complex Projective Space

The Borel picture of the cohomology ring of a flag variety gives a description as a coset space, without identifying any representatives for the classes. Lascaux and Sch\"utzenberger gave specific ...

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votes

**2**answers

145 views

### Sumsets and dilates: does $|A+\lambda A|<|A+A|$ ever hold?

The following problem is somehow hidden in this recently asked question, but I believe that it deserves to be asked explicitly.
Is it true that for any finite set $A$ of real numbers, and any real ...

**5**

votes

**3**answers

228 views

### Helly's theorem in other areas of mathematics

Are there some outstanding results using some version of Helly's theorem in a totally different area (whatever that means) than convex geometry?

**1**

vote

**0**answers

60 views

### Injectivity of the Dehn-Nielsen-Baer map?

If $S$ is a closed hyperbolic surface, is there an easy proof of the injectivity of the Dehn-Nielsen-Baer map from $\mathrm{Mod}(S)$ to $\mathrm{Out}(\pi_1(S))$, taking an element of the mapping class ...

**13**

votes

**1**answer

177 views

### What are applications of commutativity theorems for rings?

Herstein's little book "Noncommutative Rings" has a chapter called Commutativity Theorems in which he proves results like Jacobson's theorem: if a ring (associative with identity, please) has the ...

**5**

votes

**0**answers

63 views

### Free actions of non-amenable groups

Let $G$ be a locally compact, second countable, non-amenable group, let $X$ be a Haudorff space that is not necessarily compact, and let $G \curvearrowright X$ be a topological action that is free ...

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26 views

### A question on an set of 8 matrices related to the SU(3) generators

SU(2) and SU(3) differ quite a bit.
The Lie algebra of SU(2) formed by the three generators g_n is the same as the algebra formed by the SU(2) matrices/elements F_n=exp (pi * i * g_n / 2). In fact, ...

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**0**answers

84 views

### How to give a $\Delta$-complex structure?

The quotient space of a finite collection of disjoint 2-simplices obtained by identifying pairs of edges is always a surface,locally homeomorphic with $\mathbb{R^2}$.
But I am not able to prove , ...

**7**

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55 views

### One identity in Lie algebras

Let $L$ be a (non-restricted) Lie algebra over a field of prime characteristic $p,$ $UL$ be its universal enveloping algebra and $a_1,\dots, a_p \in L$ (the number of elements is equal to the ...

**4**

votes

**0**answers

56 views

### $H^s$ norm of a solution of a nonlinear Schrödinger equation

I'm reading the paper "Global existence and scattering for rough solutions of a nonlinear Schrödinger equation on $\mathbb{R}^3$ by Colliander, Keel, Staffilani, Takaoka and Tao.
They study the ...

**7**

votes

**0**answers

50 views

### A family of posets

Consider the family of all (finite) posets that can be obtained by repeatedly applying one of the following three operations (starting e.g. with the empty poset):
(O1) Disjoint union of one or more ...

**1**

vote

**0**answers

34 views

### Bounds on the spherical measure of sub-level sets of quadratic forms

I'm wondering if there are any bounds on the spherical measure of sets of the form
$$
\mu_n\left(\{y\in S^{n-1} : \frac{y_1^2}{y_2^2} < \alpha\}\right) \leq f(\alpha)
$$
where $\alpha$ is some ...

**1**

vote

**0**answers

64 views

### On the compactification of moduli space of vector bundles

Let $X$ be an irreducible, nodal curve over an algebraically closed field of genus at least $2$. Denote by $U(r,d)$ (resp. $U^0(r,d)$) the moduli space of torsion-free (resp. locally free) sheaves of ...

**7**

votes

**1**answer

72 views

### Does the Tutte polynomial of iterated cone graphs detect isomorphism?

Let $T_G(x,y)$ denote the Tutte polynomial of a graph. Of course we may have $T_G(x,y) = T_H(x,y)$ for $G$ and $H$ non-isomorphic graphs.
Now let $c(G)$ denote the cone graph of $G$, i.e., the graph ...

**1**

vote

**0**answers

26 views

### Dense subgroups in subgroups of profinite groups

Let $G$ be a finitely generated residually finite group and $\hat G$ its profinite completion.
Then for all $g\in \hat G$ we have $gGg^{-1}\leq \hat G$ is dense.
Suppose that $H\leq \hat G$ is a ...

**1**

vote

**0**answers

21 views

### Perturbation of a Fredholm sections which preserves compactness of 0-set

I am learning Morse-Bott-Floer theory and found the following cool paper
http://de.arxiv.org/abs/1310.5080
by P. Albers and D Hein. In order to prove a cup-length estimate on the number of critical ...

**0**

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**0**answers

14 views

### Tensor Algebra Quotients of the Ext-Alg of an SU(2)-Module

Let $V$ be a simple (left) $SU(2)$-module, and $T(V)$ the tensor algebra of $V$. If we quotient $T(V)$ by the ideal generated by a simple submodule of $V \otimes V$, is there a general system for ...

**2**

votes

**2**answers

109 views

### Obstruction to get a galois invariant cycle

Let $X$ be a smooth projective variety over a finite field $k$, $G=Gal(\bar{k}/k)$ and $\Gamma\in CH^i(\bar{X})$ such that:
$cl(\Gamma) \in H_{et}^{2i}(\bar{X},\mathbb{Z}_l(i))^G$ and
$\exists$ ...

**5**

votes

**1**answer

167 views

### Can ITTM recognize a non-measurable set?

Throughout the question ITTM refers to Hamkins' infinite Turing machines, though I will be interested in results related to stronger models.
Recently I was wondering, is it consistent that there is ...

**0**

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52 views

### Deduce gysin sequence via spectral sequence in Bott and Tu

In the book Differential Forms in Algebric Topology, the authors deduce the gysin sequence via spectral sequence. I cant see the reason for their following claim: To idetify the map ...

**-4**

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54 views

### find the values of xy and z [on hold]

A mathematical puzzle was asked me in an interview. but I could not answer it.
Here is the puzzle.
X Y Z
+ X Y Z
+ X Y Z
---------
Z Z Z
The sum of ...

**0**

votes

**0**answers

36 views

### Finding a “special” non singular submatrix

Given a square integer matrix $A \in M_n(Z)$ and two subsets $I, J \subset \{ 1, \ldots, n\}$, we define $A_{I,J}$ as the sub-matrix of $A$ containing the rows (resp. columns) whose index is in $I$ ...

**11**

votes

**1**answer

181 views

### minimal collapsing without GCH

Suppose $\kappa$ is a regular cardinal. Does there necessarily exist a poset $\mathbb P$ that collapses $\kappa^+$ while preserving all other cardinals?

**5**

votes

**3**answers

184 views

### Hausdorff space $X$ with $X\cong [X]^2$

Let $(X,\tau)$ be a Hausdorff space. Let $[X]^2 = \big\{\{x,y\}: x,y\in X \land x\neq y\big\}$. For $U,V\in \tau$ with $U\cap V = \emptyset$ we set $[U,V] = \big\{\{x,y\} \in [X]^2: x\in U\land y\in ...

**-4**

votes

**1**answer

120 views

### What exactly is wrong with this statement (Lucas-Penrose fallacy)? [on hold]

Statement
"For every computer system, there is a sentence which is undecidable for the computer, but the human sees that it is true, therefore proving the sentence via some non-algorithmic method."
...

**4**

votes

**2**answers

185 views

### $A \wedge A \wedge A$ in Chern-Simons

I am confused with the wedging operations of Lie algebra valued differential forms. Especially, for instance, I have some problems with the Chern-Simons 3-form
$$A \wedge dA + \frac{2}{3}A \wedge A ...

**0**

votes

**1**answer

32 views

### Graph classes which are not perfect but the stability number = clique cover numer?

I have a result for graphs whose stability number=clique cover number, which naturally includes the perfect graphs, but I'm curious about if there are other known and well-definable graph classes ...

**-3**

votes

**0**answers

25 views

### automorphism group of partially ordered by divisibillity [on hold]

We define bijection $F: \aleph \to \aleph$ as follows:
\begin{array}{l} {a|b\Leftrightarrow F(a)|F(b)} \\ {1\to 1} \end{array}
What group is Automorphism group linked to $F$?

**0**

votes

**0**answers

12 views

### is the minimum envelope of two inrersecting convex functions convex? [on hold]

when two convex cost functions intersects, can we say that their minimum envelope is convex, which doesn't looks like convex? Again if it is not convex, then is any relaxation theorem available such ...

**5**

votes

**0**answers

78 views

### The possibility of a symmetric difference in a torsion-free group

Is there a torsion-free group containing two elements $x$ and $y$ and a finite non-empty subset $B$ such that $B=xB \triangle yB$, where $\triangle$ denotes the symmetric difference of two sets and ...

**5**

votes

**1**answer

98 views

### Example of a $G$-sphere that is not a $G$-representation sphere

Let $G$ be a finite group with the discrete topology. To set terminology:
a $G$-sphere is a sphere equipped with a continuous $G$-action
a $G$-representation sphere is a $G$-sphere obtained from an ...