3
votes
3answers
425 views

Questions on 3-manifolds with a given boundary

I have the following question: For a given two-dimensional Riemann surface $C$, Is there a way to classify all topologically distinct three-dimensional compact manifolds $M$ whose boundary is $C$, ...
0
votes
1answer
336 views

pseudo-Anosov maps on surfaces with boundary

In "Automorphisms of Surfaces after Nielsen & Thurston" by Casson & Bleiler (on pages 75 - 80) they discuss classifying automorphisms of a surface. They show that, if $S$ is a closed ...
3
votes
2answers
412 views

SU(2) representations of alternating knot groups

Suppose that $K$ is an $\textit{alternating}$ knot in $S^3$, and let $R_0$ be the space of homomorphisms from $\pi_1(S^3 - K)\to SU(2)$ which send meridians to trace free matrices. Denote the subset ...
3
votes
3answers
659 views

What do you call the product of a circle and an annulus?

What would you call the product of an annulus and $S^1$ (a 'thickened' torus like 3-manifold)? More generally, is there an archive or list online of names assigned to various (non-standard) manifolds ...