# All Questions

100,225 questions
118 views

### Bicommutant theorem for commutative operator algebras

Let $\mathcal{B}(H)$ denote the space of bounded linear operators on a complex Hilbert space $H$. The von Neumann bicommutant theorem says: Theorem. Suppose that $\mathcal{A}$ is a $C^*$-subalgebra ...
154 views

### Confusion about topological Hochschild homology and $\mathbb{Z}_p$-topological Hochschild homology

Let $R$ be the ring of integers in a perfectoid field of mixed characteristic $p$. Is $\pi_*THH(R)$ (as defined in Bhatt--Morrow--Scholze) $p$-complete (as an abelian group)?
39 views

### Relating the components of the Riemann curvature tensor to the second partials of the components of the metric

I am currently reading through a proof of Proposition 6 in Chernoff's theorem and discrete time approximations of Brownian motion on manifolds OG Smolyanov, H Weizsäcker, O Wittich - Potential ...
65 views

### On the prime spectrum of $R[[X]]$ when the prime spectrum of $R$ is Noetherian

All rings below are commutative with unity. If $R$ has a.c.c. on radical ideals i.e. if $Spec R$ is Noetherian under Zariski topology, then so is $R[X]$, this is Theorem 2.5 in the following paper ...
29 views

### I want to obtain 'r' from the equation second time derivative of r is equal to a constant divided by square of r plus a constant? [on hold]

The solution expression should be like 'r=....', where the right hand side of the solution expression should not contain r. what to do? please help.
63 views

305 views

### Smooth proper variety over $\mathbb Q$ with everywhere bad reduction

$\newcommand{\Spec}{\operatorname{Spec}}$ Cross-post from Math.SE, hopefully people more knowledgeable in the field will see the question here on MO. It is a well-known fact that a smooth projective ...
72 views

### Is every orientable $I$-bundle over an orientable surface trivial?

Is every orientable $I$-bundle over an orientable surface $F$ trivial, $I \times F$? Is this also the case for vector all bundles? Similarly, is every orientable $I$-bundle over an nonorientable ...
31 views

### Continuous self-maps of the plane are semiconjugate or conjugate?

Let $f : X → X$ and $g : Y → Y$ be continuous functions. We say that $f$ and $g$ are topologically conjugate if there exists a homeomorphism $α : X → Y$ such that $$f∘α=α∘g$$. A related idea is the ...
31 views

### Enrichment of lax monoidal functors between closed monoidal categories

Let $\mathscr C,\mathscr D$ be (right) closed monoidal categories. Then both of them can be considered as enriched over themselves via their internal homs, which I will denote by $\textbf{Maps}$. Now ...
81 views

30 views

49 views

### CDF of a RV that is the ratio between a complex Gaussian and a Chi-squared RVs

Given the following p.d.f., which is the p.d.f. of the real and imaginary parts of a random variable that is the ratio between a complex Gaussian and a Chi-squared RVs: \begin{equation*} f_U(u)=\exp\...
53 views

### Sobolev embedding in complete manifold

Let $(M,g)$ be a complete Riemannian $m$-manifold, with bounded geometry and $m\geq2$. Suppose that $(M,g)$ admits a bounded geometry. Q Can we show that for $k-\frac{m}{p}\geq l-\frac{m}{q}$, we ...
115 views

24 views

### Modulus of image of a curve family in a rectangle

I don't expect to get a positive answer to this question but I may as well try. Let $R$ be the rectangle in $\mathbb{C}$ given by $\{z=x+iy: 0\leq x \leq l, 0 \leq y \leq h\}$ for some $l,h>0$. ...
54 views

### Is there a notion of tunnel number for 2-knots?

Given an embedded circle $K$ in $S^3$, the tunnel number of $K$ is the minimum number of embedded arcs one needs to add to $K$ so that the complement of $K$ and the arcs is a handlebody. For an ...
Is there a dense connected subset $X$ of the Cantor fan $$(C\times [0,1])/(C\times \{1\})$$ such that for every two connected subsets $X_1,X_2\subseteq X$, the intersection $X_1\cap X_2$ is connected? ...