All Questions
Tagged with fundamental-group rt.representation-theory
7 questions
36
votes
3
answers
3k
views
Tannaka formalism and the étale fundamental group
For quite a while, I have been wondering if there is a general principle/theory that has
both Tannaka fundamental groups and étale fundamental groups as a special case.
To elaborate: The theory of ...
- 4,450
23
votes
3
answers
2k
views
How bad can $\pi_1$ of a linear group orbit be?
Let $G$ be a simply connected Lie group and $\mathcal O= G(v)=G/G_v$ a $G$-orbit in some finite-dimensional $G$-module $V$. By the homotopy exact sequence, its fundamental group $\Gamma$ is the ...
- 31.5k
8
votes
1
answer
850
views
Representation theory of higher homotopy groups
I've seen some works on the representation of fundamental groups, which are (at least for me) quite important topic in mathematics. For example, Riemann-Hilbert correspondence relates representation ...
- 2,215
8
votes
0
answers
373
views
$p$-adic representations of the fundamental group of a smooth proper curve over a finite field
This question is very general. Let $C$ be a smooth and proper curve over a finite field ${\bf F}_p$. Are there any general results or conjectures on continuous non abelian representations
$$
\pi_1(C)\...
- 3,076
7
votes
1
answer
229
views
Why is the fundamental group of $\mathsf E_n$ cyclic of order $9 - n$?
Several years ago, I mentioned offhandedly to a colleague that I had noticed that, if you extend the $\mathsf E_n$ series downwards in the natural way, by removing nodes from the long arm of $\mathsf ...
- 12.9k
5
votes
2
answers
756
views
explicit linear representations of fundamental groups of surfaces
I am looking for an explicit representation of the fundamental group of a closed orientable surface of genus >1. I guess they should be abundant in degree 2. Did anyone see the explicit matrix ...
- 1,050
1
vote
1
answer
329
views
$P^1$ minus k points
For $k\geq 3$, and $k$ arbitrary points $S=( z_1,\cdots,z_k ) \in \mathbb{P}^1$, we can write
$$ P^1 \setminus S \cong \mathbb{H}/G $$
where $\mathbb{H}$ is the upper-half plane and $G\subset PSL(2,...
