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Jan
27
revised Uniform continuity of length function on geodesic currents
Improving the very confusing notation (two identical C's)
Jan
21
revised Subgroups of the mapping class group of a surface generated by Dehn twists
fix typo
Jan
21
revised Subgroups of the mapping class group of a surface generated by Dehn twists
made notation a bit more pretty.
Jan
21
revised Subgroups of the mapping class group of a surface generated by Dehn twists
much more detail
Jan
20
comment Subgroups of the mapping class group of a surface generated by Dehn twists
Dear Rémi - Ah, yes - I see your point. I'll edit my answer. But the papers I referenced are still what you want - those techniques will give you examples of the kind you want.
Jan
19
answered Subgroups of the mapping class group of a surface generated by Dehn twists
Jan
17
revised Classification of knots by geometrization theorem
Refs to Matveev, snappy. Credit where due.
Jan
17
revised Classification of knots by geometrization theorem
Refs to Matveev, others. Credit where due.
Jan
17
comment Classification of knots by geometrization theorem
Dear Igor - Fair point - I'll edit my answer. However, we can't say that the answer was "written down by Hemion". His book is actively wrong in many places. See Scharlemann's MathSciNet review of the book.
Jan
16
revised Classification of knots by geometrization theorem
better links
Jan
16
answered Classification of knots by geometrization theorem
Jan
10
comment Judging whether a finitely presented group is a 3-manifold group?
Thinking about homology considerations tells us that the longitude of X is glued to the longitude of Y - that reduces the set of possible gluings to a "line" of Dehn twists. I think that your "challenge" could now be answered computationally if we had a facility to glue manifolds with torus boundary. Does that exist?
Jan
10
comment Judging whether a finitely presented group is a 3-manifold group?
If I haven't made a mistake: I used a variety of tools, ending with snappy, to obtain a triangulation of this three-manifold M. I then used regina to find fundamental normal tori. Cutting proves that M is obtained by gluing X, the figure eight knot complement, to Y, the Seifert fibered space with base orbifold D(2,2) (aka the orientation I-bundle over the Klein bottle). Unfortunately, regina doesn't track gluing data when we cut along a normal torus. So we can't recover the gluing data that way.
Dec
14
comment Heegard genus of hyperbolic Haken 3-manifolds
@VandersonLima - After seeing your comment, I thought to check KnotInfo. It says that 57 of the 135 knots (as in Ken Baker's comment) are fibered. Jesse's construction will give you infinitely more examples of the kind you asked for, but they won't all be fillings of knots in the three-sphere.
Dec
13
comment Is the following 3-manifold always a trivial I-bundle over a surface?
@IgorRivin - Yes, correct. But we wouldn't want to waste a good weasel!
Dec
11
awarded  Revival
Dec
11
answered Heegard genus of hyperbolic Haken 3-manifolds
Dec
11
comment Is the following 3-manifold always a trivial I-bundle over a surface?
@IgorRivin - Sure. But the original poster might want to avoid using a giant hammer of a theorem, when a tiny spatula of an assumption will do the same job.
Dec
11
revised Is the following 3-manifold always a trivial I-bundle over a surface?
last change, I hope.
Dec
11
answered Is the following 3-manifold always a trivial I-bundle over a surface?