# All Questions

103,080 questions

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### Is it true that $$( V \otimes^{max}W)^+=V^+ \otimes^ {max} W^+$$

For any $C^*-$ algebra $V$ assume that $V^+$ denotes the unitization of $V$. Let $V$ and $W$ be two $C^*-$ algebras then is it true that $$( V \otimes^{max}W)^+\cong V^+ \otimes^ {max} W^+$$
I guess ...

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12 views

### Dense Stein subset in complex manifold

Let $X$ be a smooth proper algebraic variety. Then $X$ has a dense affine open subset. In particular, any smooth proper algebraic variety has a dense Stein open subset as the complement of a divisor.
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12 views

### Find a strong connected components for the graph [on hold]

I need a help with a homework of discrete mathematics, I’ll be really grateful for anyone who will be able to help me
https://3.top4top.net/p_1245ww3160.jpg
Thanks for everybody

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45 views

### First homology group of the general linear group

The abelianization of the general linear group $GL(n,\mathbb{R})$ defined by $GL(n)^{ab} := GL(n)/[GL(n), GL(n)]$ is isomorphic to $\mathbb{R}^{\times}$. This follows from the fact that $[GL(n),GL(n)] ...

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16 views

### About the Zassenhaus's filtration of a group G

The $n$-th term of the filtration of Zassenhaus of a group $G$, denoted by $D_n(G)$, is the subgroup generated by all $p^k$-th power of an element $x\in \gamma_i(G)$ such that $ip^k$ is greater or ...

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**1**answer

44 views

### Non-standard tensor products of inner product spaces

For two inner product spaces $(\mathcal{V}, (\cdot,\cdot)_V)$ and $(\mathcal{W}, (\cdot,\cdot)_W)$, we can put an inner product on their tensor product in the obvious way:
$$
(1) ~~~~ \langle v \...

**2**

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**2**answers

133 views

### Tricks for getting a creative idea [on hold]

Caveat: I fear that people will criticize me for asking this potentially inappropriate question here, but I guess that the community here is quite unique in the ability of potentially answering my ...

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39 views

### When is Fun(X,C) comonadic over C with respect to the colimit functor?

Because I'm primarily interested in this question from the point of view of $\infty$-categories (in this case, modeled by quasicategories), I'll ask this question using that terminology. In particular,...

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27 views

### Sub-Gaussian decay of the measure of Euclidean balls

Let $X$ be a random vector in $\mathbb{R}^d$ satisfying the following property: there exists $C_1,C_2>0$ such that
$$\int_0^{+\infty}\mathbb{P}(\|X-\mu_0\|\leq\sqrt{t})\exp(-t)dt\leq C_1\exp(-C_2\|\...

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35 views

### How can I solve this issue?

I have a problem related to this theme system analysis and action research. If you can please solve this, in another case please take me more resource for understanding this.
The system consists of N-...

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84 views

### Greatest prime factor of n and n+1

For a positive integer $n$ we denote its largest prime factor by $\operatorname{gpf}(n)$. Let's call a pair of distinct primes $(p,q)$ $\textbf{nice}$ if there are no natural numbers $n$ such that $\...

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**1**answer

52 views

### HTTP GET request in math [on hold]

How would I go about making an HTTP GET request? I've tried looking at Curl for math, but it just doesn't provide enough information. Can I do something like this?
$d = g([S,O,M,E,U,R,L])$
Thanks.

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57 views

### The cobordism hypothesis, and the bordism n-category as a free construction

In this question, I write $\text{Bord}_n$ for the symmetric monoidal $n$-category of framed n-bordisms, and $\text{D}_n$ for the free symmetric monoidal $n$-category with all duals on the terminal ...

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23 views

### Holomorphic maps from upper half plane to itself (or equivalently Poincare disc to itself)

Suppose I parametrize complex plane by coordinates,$$z = x+i y,\ \bar z=x-i y$$
then the upper half plane, $\mathbb H_+$ is given by $y>0$. I am looking for chiral coordinate transformations, $f(z)$...

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37 views

### Projection of an invariant almost complex structure to a non-integrable one

My apologies in advance if my question is obvious or elementary.
We identify elements of $S^3$ with their quaternion representation $x_1 + x_2i + x_3j + x_4k$. We consider two independent vector ...