MathOverflow

I was reading the paper “On two topologies that were suggested by Zeeman” by Papadopoulos and Papadopoulos. In Theorem 1.1, the authors show that the group of homeomorphisms of Minkowski space coincides with the group of automorphisms of this space.
In light of this result, is it possible to define a topology on a manifold such that a transformation group acting on it is exactly the same as its homeomorphism group?...

Let $K=\mathbb{Q}_3(t)$ be the finite extension of the $3$-adic number field $\mathbb{Q}_3$, where $t=3^{1/13}$. I want to know if the polynomial $$f(x)=(x^9-t^2)^3-3^4x+3^3t^5 \in K[x]$$ reducible or not.
Method 1: If $v_3$ is the normalized valuation $v_3(3)=1$, then $v_3(t)=\frac{1}{13}$ as $t^{13}=3$. Let us find the Newton polygon, whose vertices are $(27,0), (28, 15/13), (9, 17/13), (1,4), (0, 6/13)$ ....

Has anyone used the Joni-Rota-Godsil integral formula (see details below) to count perfect matchings of square-grid graphs, Aztec diamond graphs, hexagon-honeycomb graphs, etc.? (Or even just to count perfect matchings of the 2-by-$n$ grid?)
I suspect that the answer is "no", since the method seems to implicitly involve the whole matching polynomial (instead of restricting to perfect matchings), and I don't think that the matching polynomials of these graphs are particularly tractable (though...

Let $A = \ell^1(G)$ be the convolution Banach $*$-algebra of a finite (not necessarily abelian) group $G$ with norm $\|\cdot\|_1$,let $\mu \in A$ be a probability measure, and set $\delta = \|\mu * \mu - \mu\|_1 \leq 1/10$.Is it the case that there must...