Sam Nead
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Registered User
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Apr 27 |
answered | Mid point with set square? |
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Mar 30 |
accepted | if $S \times \Re$ is diffeomorphic to $T \times \Re$ then are S and T diffeomorphic? |
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Mar 29 |
answered | if $S \times \Re$ is diffeomorphic to $T \times \Re$ then are S and T diffeomorphic? |
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Mar 23 |
answered | If a graph embeds in the projective plane or the torus is there a bound on the number of edge crossings it has in the plane? |
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Mar 20 |
awarded | ● Nice Answer |
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Mar 17 |
accepted | Triangulation of moduli space. |
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Mar 17 |
answered | Triangulation of moduli space. |
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Mar 16 |
accepted | Two solid N_3 glued by its boundary |
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Mar 6 |
accepted | Once punctured torus bundles in snappy/twister |
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Mar 6 |
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Once punctured torus bundles in snappy/twister I believe the twister page is not relevant -- the b++ etc is "classic" SnapPea notation. |
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Mar 6 |
answered | Once punctured torus bundles in snappy/twister |
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Mar 2 |
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Are there replacements for the curve complex that make up for its weaknesses? Finding geodesics in the curve complex is algorithmic, due to work of Leasure (his thesis) and independently, Shackleton. |
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Mar 2 |
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What is the isometry group of $AD(V)$? What is the definition of a "spanning annulus"? Note that any annulus in a handlebody is either compressible or boundary compressible, so the "right" class of annuli may be a bit difficult to chose. For example, do you want to rule out boundary parallel annuli? |
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Mar 2 |
answered | the carrier graph and Heegaard surface |
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Feb 22 |
revised |
Is integer GCD in NC? fixing links, take two |
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Feb 7 |
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Hyperbolic 3-manifolds with no geometrically finite structure [See page 14, paragraph (3) of Hatcher's notes.] Basically, if a boundary torus $T$ compresses, then there is a disk $D$ with various properties. Take a neighborhood $K$ of $T \cup D$ and consider the frontier of $K$ in the manifold $M$. This will be a sphere and so bound a ball in $M$, by irreducibility. Thus $M$ is a solid torus. |
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Feb 7 |
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Hyperbolic 3-manifolds with no geometrically finite structure @Igor - Not quite! For example, the solid torus $S^1 \times B^2$ is irreducible and atoroidal (and hyperbolizable!) but the boundary torus is compressible. There are also Seifert fibered spaces which satisfy the hypothesis and conclusion, but that are of course not hyperbolic. |
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Feb 7 |
accepted | Hyperbolic 3-manifolds with no geometrically finite structure |
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Feb 7 |
revised |
Hyperbolic 3-manifolds with no geometrically finite structure Answering Igor's actual (?) question, linking to Hatcher. |
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Feb 7 |
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Hyperbolic 3-manifolds with no geometrically finite structure I will add a reference to my answer. |
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Feb 7 |
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Hyperbolic 3-manifolds with no geometrically finite structure There is a purely geometric proof, as well. Suppose $N$ is hyperbolic, and $B_S$ and $B_T$ are disjoint horo-tori about $S$ and $T$. Suppose that $A$ is a compact annulus connecting $B_S$ to $B_T$. Lift everything to the universal cover. A component of the lift of $A$ is a strip (quasi-isometric to a line!) that fellow-travels lines in two distinct horospheres, a contradiction. |
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Feb 7 |
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Hyperbolic 3-manifolds with no geometrically finite structure There are lots of copies of $Z^2$ in $\pi_1(K)$ and all of them have to be parabolic. This leads to contradictions. |
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Feb 7 |
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Hyperbolic 3-manifolds with no geometrically finite structure @Igor - I suggest you ask this (new, to my eyes) question in a separate post. However, very briefly, a hyperbolic manifold is algebraically atoroidal - that is, any $Z^2$ subgroup is parabolic. [This is an exercise in hyperbolic geometry, using the discreteness of the group.] Let's now do just one of the many cases. Suppose that $S$ and $T$ are boundary tori, and $A$ is an annulus between them. Let $K$ be a small neighborhood of $S \cup A \cup T$. Then $K$ is homeomorphic to $P \times I$ where $P$ is a pair of pants. So $\pi_1(K)$ is a rank two free group, crossed with $Z$. |
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Feb 7 |
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Hyperbolic 3-manifolds with no geometrically finite structure Cleaning up the logic. |
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Feb 7 |
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Hyperbolic 3-manifolds with no geometrically finite structure Because Theorem 19.6 is a different path to proving the hyperbolization theorem. See the remarks immediately after the proof of Theorem 15.3, at the top of page 372. |
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Feb 7 |
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Hyperbolic 3-manifolds with no geometrically finite structure (@Bruno - One last case: the new torus is parallel into the boundary.) |
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Feb 7 |
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Hyperbolic 3-manifolds with no geometrically finite structure My last comment doesn't use anything from the theory of Kleinian groups. It is instead part of the JSJ theory. |
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Feb 7 |
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Hyperbolic 3-manifolds with no geometrically finite structure added 110 characters in body |
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Feb 7 |
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Hyperbolic 3-manifolds with no geometrically finite structure If the manifold has tori in the boundary, and has an essential cylinder connecting torus boundary components (or connecting a torus boundary component to itself) then the manifold is algebraically toroidal (and thus geometrically toroidal or small Seifert fibered). |
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Feb 7 |
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Hyperbolic 3-manifolds with no geometrically finite structure @Igor - Yes. The paring locus can be empty! |
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Feb 7 |
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Hyperbolic 3-manifolds with no geometrically finite structure You are correct - I was referring to the wrong thing. I have added a temporary fix, and will look for a precise reference. |
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Feb 7 |
revised |
Hyperbolic 3-manifolds with no geometrically finite structure FIxed large mistake! |
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Feb 7 |
answered | Hyperbolic 3-manifolds with no geometrically finite structure |
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Feb 2 |
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Applications of knot theory Is this a question or a suggestion? Any references you could point me to would be very much appreciated. |
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Jan 30 |
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Growth zeta-functions of regular languages Actually, reading Krob more closely, he passes the buck to Volume A, Chapter 8 of "Automata, languages, and machines". This is a pretty cryptic book, unfortunately. The following question and answer seems relevant: mathoverflow.net/questions/45149/… |
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Jan 30 |
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Growth zeta-functions of regular languages Ok - You can make this answer correct by adding the hypothesis that the RE is "unambiguous". This concept appears to be nicely set out in lecture notes of Daniel Krob, in French, available here: lix.polytechnique.fr/~dk -- see Definition 1.1.3. If anybody knows an English version of this material, I would be very interested... |
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Jan 29 |
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Growth zeta-functions of regular languages I up-voted this, and then realized that I actually don't understand this answer. For example. a*+a* = a*, so the growth functions are the same. This answer suggests that the LHS has twice the growth of the RHS. So there is something funny going on. (You can certainly replace disjoint union with addition.) Likewise, something funny is going with (E*)* = E*.... |
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Jan 2 |
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What are conjectures that are true for primes but then turned out to be false for some composite number? @domotorp - Why does this have the gt tag? |
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Dec 14 |
accepted | The action of torsion of $MCG(S)$ on curve complex |
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Dec 14 |
answered | The action of torsion of $MCG(S)$ on curve complex |
