MathOverflow

The tubular neighbourhood theorem, stating that an embedded submanifold has a neighbourhood that is a diffeomorphic image of an open subset of the normal bundle, is a staple result about smooth manifolds. There is no version in the complex analytic category...

I am looking up at the book of Yves Myers "Algebraic Numbers and Harmonic Analysis" where, in a serious treatment of Pisot numbers, they used this particular lemma without proof.
The conditions (under which we are trying to investigate) of this lemma are as follows: $\alpha, \beta, a, b$ are real numbers where the numbers $b,a$ are different from $0$ and also $b/a$ is irrational, and $|a\beta - \alpha b| \neq 0$. We let $l: ...

I will try to demonstrate the problem with a trivial example:
Suppose that there is traffic a light with the usual three distinct colors: Red, White and Green. The traffic light will switch on one light at random at the end of each day.
The probabilities associated with each light being switched on at the end of each day are determined by some exogenous process every morning: and once these probabilities are determined, they become known. So every morning, we have a probability measure...

Freed and Hopkins use the spectrum $I\mathbb C^\times$ to define the target of discrete invertible field theories. I have trouble understanding, how this arises. Naively, physically, I would think that its connective covers should be equivalent to the...