All Questions
4 questions
21
votes
6
answers
3k
views
Is there a good notion of morphism between orbifolds?
Following Thurston, an orbifold is a topological space which looks locally like a finite quotient of $\mathbb R^n$ by a finite group of $O(n)$: this is expressed using charts as for differentiable ...
3
votes
1
answer
323
views
When is an irreducible $\mathrm{SL}_2(\mathbb{C})$ representation of a cusped hyperbolic 3-manifold scheme reduced or smooth?
Let $M$ be an orientable cusped hyperbolic 3-manifold. Let $\rho \in \mathrm{Hom}(\pi_1(M),\mathrm{SL}_2(\mathbb{C}))$ be an irreducible representation.
Is $\rho$ scheme reduced ?
What can ...
15
votes
1
answer
1k
views
Can the SL_2 character variety of a three-manifold be nonreduced?
Let $M^3$ be a three-manifold and consider the representation variety and the character variety of $M$:
$$Y=\operatorname{Hom}(\pi_1(M^3),\operatorname{SL}(2,\mathbb C))$$
$$X=\operatorname{Hom}(\pi_1(...
3
votes
0
answers
334
views
What is the behaviour of a smooth 3-manifold acting by a circle?
As Mumford pointed out in his paper 'Topology of Normal Singularities and a Criterion for Simplicity'(1961), every point $p$ on a normal complex surface $V$ has an associated 3-manifold $M$ which is ...