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A three-manifold is a space that locally looks like Euclidean three-dimensional space

3 votes
2 answers
463 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 $\chi(F)=n(\chi(B)-\sum_i^r\frac{a_i-1}{ …
1 vote

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

that corresponds to the complement of a trivial (but essencial) torus knot in a open solid torus. For those -Fico had mention- they are called cable spaces and have nice foliation into circles. Its na …
janmarqz's user avatar
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3 votes
3 answers
761 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
3 answers
744 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 …