0
votes
0answers
27 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 ...
7
votes
0answers
45 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 ...
2
votes
0answers
19 views

Free actions of non-amenable groups

Let $G$ be a locally compact, second countable, non-amenable group, let $X$ be a metric space that is not necessarily compact, and let $G \curvearrowright X$ be a topological action that is free ...
0
votes
0answers
15 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, ...
0
votes
0answers
51 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 , ...
4
votes
0answers
37 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 ...
3
votes
0answers
34 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 ...
6
votes
0answers
35 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 ...
0
votes
0answers
19 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
0answers
53 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 ...
4
votes
0answers
27 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 ...
0
votes
0answers
21 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
0answers
15 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
votes
0answers
13 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
2answers
77 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
1answer
99 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
votes
0answers
45 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
votes
0answers
41 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
0answers
31 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 $I$ ...
9
votes
1answer
129 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?
4
votes
3answers
125 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
1answer
112 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
2answers
167 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
1answer
27 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
0answers
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
0answers
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
0answers
64 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
1answer
93 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 ...
3
votes
0answers
72 views

Reference for Grothendieck's duality and Cousin, Dualizing and Residual complexes

I am a graduate student currently reading Hartshorne's Residues and Duality. In order to reach the construction of the right adjoint $f^!$ of $Rf_*$ for some special types of maps of locally ...
4
votes
1answer
88 views

Why the term “geometric” rough path?

A "geometric" rough path is a rough path such that $Sym(\mathbb{X}_{s,t})=\frac{1}{2}X_{s,t}\otimes X_{s,t}$. For example the Ito rough path is not geometric because ...
4
votes
1answer
70 views

Loss of derivative of subelliptic operator

Consider the differential operator $P$ on $\mathbb{R}^2$, given by $P = \frac{\partial^2}{\partial x^2} + x^2\frac{\partial^2}{\partial y^2}$. Clearly it is elliptic everywhere except on the $y$-axis. ...
-5
votes
0answers
48 views

Genus formula for a curve in a $2$-dimensional complex torus? [migrated]

For a curve $C$ in a $2$-dimensional complex torus $T$, is there any formula to compute the genus of $C$? Say, in terms of self-intersection number? For a curve in $\mathbb{P}^2$ or a K3 surface, ...
4
votes
0answers
40 views

O-Minimal sentences in $L_{\omega_1,\omega}$?

Is there any meaningful sense in which we can talk about o-minimal sentences of $L_{\omega_1,\omega}$? I can give a first attempt, easily; given a countable fragment $F$ and a sentence $\Phi$ in that ...
0
votes
0answers
34 views

Find all possible rational pairs of a parametric sextic and all cases where it is reducible for either parameter

Find all possible rational solutions pairs $(z,a)$ of the equation $a^6 + a^4 (-18368 + 9184 z - 2912 z^2) + a^2 (61702144 - 61702144 z + 36814848 z^2 - 10694656 z^3 + 1748992 z^4) - z^2 ...
2
votes
0answers
31 views

Sequences of transition probability measures

Suppose that $X$ and $Y$ are compact metric spaces. A Borel probability measure $\mu$ on $X\times Y$ satisfies $$ \mu(A\times B)=\int_A\mu(B|x)\mu_X(dx), $$ for $A$ and $B$ Borel sets in $X$ and $Y$ ...
0
votes
0answers
15 views

Non-uniform matroids as the matroid sum of uniform matroids

Can all non-uniform matroids be written as the direct sum / matroid sum of uniform matroids? If so, What happens to the matrices representing the uniform matroids? If the non-uniform matroid is ...
5
votes
3answers
528 views

Catalan numbers as sums of squares of numbers in the rows of the Catalan triangle - is there a combinatorial explanation?

This question arose from an answer to my recent question How many traces are there on Temperley-Lieb, Fuss-Catalan, Iwahori-Hecke, Birman-Wenzl-Murakami-Kauffman, ... algebras? What I need from that ...
-2
votes
0answers
19 views

For which $x$ the inequality $ax+be^{x/2}>c$, where $a,b,c,x>0$ and $c>2b$ holds [migrated]

For which $x$ the inequality $ax+be^{x/2}>c$, where $a,b,c,x>0$ and $c>2b$ holds. Can someone help me for this. Thank you.
0
votes
0answers
5 views

The minimum perimeter and maximum height of a triangle under constraints [migrated]

I do not get the following formulas : ...
0
votes
0answers
11 views

Is there a field in which every rational polynomial has a root (other than the obvious fields)? [migrated]

Let $\mathbb{A} \subset \mathbb{C}$ denote the field of numbers algebraic over $\mathbb{Q}$. Is there a proper subfield $F$ of $\mathbb{A}$ such that every nonconstant polynomial $p(x) \in ...
0
votes
0answers
48 views

Condition to obtain a not compact embedding

I have the two spaces $W_0^{1,p}$ with the norme $$||u||^p=||u||^p_{L^p}+||\nabla u||^p_{L^p}$$ and $$L^{p^*}_{\alpha}=\{ u~\text{measurable}, \int_{\Omega} (|x|^{\alpha} u(x)|)^{p^*} dx<\infty\}$$ ...
5
votes
0answers
98 views

Rankin-Selberg for Maass form GL(3)xGL(2)

Let $F$ be a Maass cusp form for $\mathrm{SL}(3,\mathbb{Z})$ (level 1 trivial character). Let $g$ be a Maass cusp form for $\Gamma_0(N)$ with character $\chi$ mod $N$. For convenience, you may assume ...
0
votes
0answers
39 views

Epsilon-net of operator norm ball around Identity

Suppose I look at the set of matrices which are invertible and satisfy $$ \left\|A-Id\right\|_{op}<r $$ for some $r<1$, where $Id$ is the $n\times n$ identity matrix. An $\epsilon$-net of such ...
-1
votes
0answers
37 views

Martingale definition [on hold]

To prove that one process is Martingale, generally we prove 3 things : 1) X is adapted. 2)$$ \mathbf{E} ( \vert X_n \vert )< \infty $$ 3) $$\mathbf{E} (X_{n+1}\mid X_1,\ldots,X_n)=X_n $$ I ...
3
votes
5answers
270 views

classification of $p$-groups

I have two questions regarding to $p$-groups. A $p$-group $G$ is said to be extraspecial of $G'=Z(G)$ has order $p$. Hence extraspecial groups are examples of $p$-groups with cyclic center. Of ...
2
votes
0answers
96 views

On Abelian Galois Covering

Consider a complete quadrangle $\Delta$ in $\mathbb{CP}^2$ (i.e. the union of the six lines through points $P_1$, $P_2$, $P_3$ and $P_4$ in general position). Let $f: Y := \hat{\mathbb{CP}^2}(P_1, ...
1
vote
0answers
43 views

Arc Sine law for Random Walk conditioned to non-absorption or not?

Let $S_n$ be simple symmetric Random walk on the integers in $[-N,N]$ with states $N$ and $-N$ absorbing. Let $\tau$ be the time to absorption when $S_0 = 0$. Is the $E(S^{2}_{n}| \tau \geq n)$ ...
7
votes
1answer
89 views

Decompose dependent random variables into function of dependent and independent parts

Let $X$ and $Z$ be two (possibly dependent) random variables. Is it necessarily the case that there exists a Borel function f and a random variable $Y$ that is independent of $X$ such that $Z = f(X, ...
3
votes
0answers
98 views

What are the indecomposable classes on a del-Pezzo surface?

Let $X_k$ be $\mathbb{P}^2$ blown up at $k$ points (where $k$ is $0$ to $8$). Let $\beta \in H_2(X_k, \mathbb{Z}) $ be a homology class given by $$ \beta := n L + m_1 E_1 + \ldots + m_k E_k $$ ...
0
votes
0answers
14 views

Number of Nodes in energy eigenstates [migrated]

I have a question from the very basics of Quantum Mechanics.Given this theorem: For the discrete bound-state spectrum of a one-dimensional potential let the allowed energies be $E_1<E_2< ...

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