MathOverflow Questions, Problems & Solutions : TransWikia.com ~ Page 29

triviality of homology with local coefficients

Let $X$ be a manifold or a CW-complex. Let $pi: tilde Xlongrightarrow X$ be a covering map. Let $pi_1(X)$ be the fundamental group of...

Asked on 02/17/2021

1 answer

Generators of sandpile groups of wheel graphs

In the paper "On the Sandpile Group of a Graph" by Cori and Rossin one can find a result related to the structure of the sandpile group...

Asked on 02/16/2021 by castor

1 answer

Conditions for pointwise convergence of indicators precomposed with uniformly continuous sequence

Let $X$ be a compact metric space, ${delta_n}_{n=1}^{infty}$ be a strictly monotonically decreasing sequence in $[0,1]$ converging to $0$, and ${h_n}_{n=1}^{infty}$ be a uniformly convergence...

Asked on 02/16/2021 by Bernard_Karkanidis

1 answer

(Weakly) connected sets with large (out-)boundary

Let $Gamma=(V,E)$ be a connected undirected graph with n vertices such that every vertex has degree at least $4$. Now draw arrows on some of the edges, in...

Asked on 02/15/2021

0 answer

Global minimum of sum of a non-convex and convex function, where minima of the non-convex function can be found

I'm interested in finding $argmin_{x in X} (f(x) + lVert xrVert_2^2)$ where $X$ is a $[0,1]^n$, $f$ is Lipschitz but non-convex and we already have a...

Asked on 02/15/2021 by Proof by wine

0 answer

Hilbert class field of Quadratic fields

Is there any method to find the Hilbert Class field of quadratic fields? Is there any bound for their dimensions? For example, if $4|d-1$ then $Q(sqrt{d},i)$ is contained in the...

Asked on 02/14/2021 by Sina

1 answer

The variety induced by an extension of a field

If $K$ is a finitely generated field extension of $k$, then there exists an irreducible affine $k$-variety with function field $K$. The idea is that if...

Asked on 02/12/2021 by Federico Fallucca

2 answer

Why is this algebra called the q-Weyl algebra?

Recall that the (first) Weyl algebra over $mathbb{C}$ is the algebra generated by $x,y$ with the relation $yx-xy=1$. It can be realized as the algebra of polynomial...

Asked on 02/12/2021 by GMRA

1 answer

Cohomology of a simplicial abelian group $X_bullet$, where $S_n$ acts on $X_n$

Let FinCar denote the category whose objects are the finite cardinal numbers $[n]={0,dots, n}$ and whose morphisms are all functions between them, and let $X$ be a...

Asked on 02/12/2021 by Patrick Nicodemus

1 answer

Hyperplane arrangements whose regions all have the same shape

Suppose I have a (finite, real, central, essential) hyperplane arrangement $mathcal{H}$ such that all regions "have the same shape": for any two regions $R,R'$, there is an orthogonal...

Asked on 02/12/2021 by Christian Gaetz

1 answer

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