MathOverflow

It is proved in the paper Symmetric completions and products of symmetric matrices that the group $\mathfrak{S}$ generated by symmetric matrices in $\operatorname{SL}_2(\mathbb{Z})$ is not the whole group, but rather equal to $\langle -I_{2 \times 2...

Let $p$ be a prime number, and let $G$ be a pro-$p$ group with finitegenerator rank $d(G)$ and finite relation rank $r(G)$. If $G$ satisfies the Golod--Shafarevich condition $r(G) < d(G)^2/4$and has $d(G) \ge 2$, then by a result of Efim Zelmanov...

Let $M$ be a smooth closed manifold. $N(M)$ be the set of normal invariants. $N(M) \cong [M,G/O]$ or $[M,G/Top]$ depending on context of $Diff$ or $TOP$ category. How does this isomorphism behaves with spherical fibration. i.e. $f: E \to M$ be a spherical...

Some questions about the paper
Lange, Herbert, Universal families of extensions, J. Algebra 83, 101-112 (1983). ZBL0518.14008."
Let $X$, $Y$ denote coherent schemes over $\mathbb C$, $f:X\to Y$ a flatprojective morphism (but proper works as well), and $\mathcal F$,$\mathcal G$ coherent sheaves on $X$, flat on $Y$. Then${\rm Ext}^i_f(\mathcal F,\mathcal G)$ is defined as the sheaf...