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13 votes
4 answers
2k views

The ten most fundamental topics in geometric group theory

What are the ten most fundamental topics in geometric group theory? This is a pedagogical question prompted by the fact that I am teaching geometric group theory to undergraduates. They are expected ...
5 votes
1 answer
239 views

Galois action on Borovoi's algebraic fundamental group

In Borovoi's paper Abelian Galois cohomology of reductive groups, the algebraic fundamental group of a connected reductive group $G$ over a field $K$ of characteristic zero is defined as $$\pi_1(G, T):...
Fu Chenji's user avatar
-4 votes
1 answer
163 views

What are all the complex structures on $\mathbb{R}^2$ which live inside $\mathrm{SL}_2(\mathbb{Z})$? [closed]

By "complex structure" I am referring to 2x2 matrices which square to $-\mathrm{Id}_2$. I need to know those with integer entries and determinant equal to 1. Thank you
nayreel's user avatar
0 votes
1 answer
120 views

Can we construct an isomorphism between $\mathrm{BS}(1,n)$ and $\mathbb{Z}[1/n]\rtimes\mathbb{Z}$ such that it preserve the order?

It is given in Regular left-orders on groups that the solvable Baumslag-Solitar group $\mathrm{BS}(1,n)=\langle a, b\mid aba^{-1}=b^n\rangle $ is isomorphic to $\mathbb{Z}[1/n]\rtimes \mathbb{Z}$ for ...
navashree chanania's user avatar
-3 votes
0 answers
157 views

A presentation for the group $GL(n,\mathbb{Z}_p)$

Let $n\ge 2$. Let $p$ be a prime and $\mathbb{Z}_p$ denote the finite field with $p$ elements. I want to know about the presentation for the group $GL(n,\mathbb{Z}_p)$ consisting of its generators and ...
SPDR's user avatar
  • 103
2 votes
0 answers
65 views

Classification of centralizers of elements of finite simple groups of Lie type

I am currently studying the twisted Ree finite simple groups given by $^2G_2(3^{2n+1})$ and I was wondering if there is a reference for the classification of centralizers of elements in this family of ...
MAP's user avatar
  • 71