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8
votes
1answer
537 views

$Spin^c$-Dirac-operator on the 3-torus

Consider the spinc structure on the flat standard 3-torus, which you get from the trivial (or any other) spin structure. Its associated vector bundle can be identified with a trivial bundle with fibre ...
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 ...
6
votes
2answers
469 views

A conjecture of Montesinos

Not every orientable 3-manifold is a double cover of $S^3$ branched over a link. For example, the 3-torus isn't. However, in 1975 Montesinos conjectured (Surjery on links and double branched covers of ...
2
votes
2answers
402 views

Branched coverings over orbifolds with reflector lines

It is well known that if $F\to B$ is a $n$-finite branched covering over an orbifold with cone-points then the orbifold Euler's characteristics are related via ...
6
votes
1answer
292 views

Residual finiteness for graph manifold groups

Is there a simple proof that 3-dimensional graph manifolds have residually finite fundamental groups? By "simple" I mean the proof that does not use any hard 3d topology. I care because I wish to ...
12
votes
6answers
2k views

Diffeomorphism of 3-manifolds

Surgery theory aims to measure the difference between simple homotopy types and diffeomorphism types. In 3 dimensions, geometrization achieves something much more nuanced than that. Still, I wonder ...
10
votes
3answers
795 views

Flat SU(2) bundles over hyperbolic 3-manifolds

Can someone give me a non-trivial example of a flat SU(2)-connection over a compact orientable hyperbolic 3-manifold? The literature on such bundles over 3-manifolds is huge and my naive searches ...
5
votes
2answers
350 views

Contracting maps of hyperbolic manifolds

Is it possible for SOME positive $c$, $c<1$ to find a pair of COMPACT hyperbolic manfiolds $M^3$ and $N^3$ with a positive degree map $$f: M^3 \to N^3,$$ such that $f$ is contacting with constant ...
2
votes
3answers
571 views

Reducible 3d torus bundles

Here reducible means that the mapping class for the fiber is a reducible auto-homeomorph in the sense of Nielsen-Thruston. So, could anyone give me a hint to classify them? In contrast, do you agree ...
2
votes
3answers
650 views

Two solid N_3 glued by its boundary

Let $N_3$ be the genus three non orientable surface. Do we have an analogous 3d manifold as the solid torus and the solid Klein bottle for $N_3$? I don't see how to extend the ideas related to the 3d ...