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Results tagged with gt.geometric-topology
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user 18496
Topology of cell complexes and manifolds, classification of manifolds (e.g. smoothing, surgery), low dimensional topology (e.g. knot theory, invariants of 4-manifolds), embedding theory, combinatorial and PL topology, geometric group theory, infinite dimensional topology (e.g. Hilbert cube manifolds, theory of retracts).
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108
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Distance at least $n$ geodesics on surface
everyone. Let $S$ be a closed orientable 2-surface with genus at least 2. Let
$\{C_{i}\mid i=1,...,3g-3\}$ be a pants decomposition of $S$. Suppose that $\{l_{C_{i}},\tau_{C_{i}}, for~ i=1,...,3g-3\} …
- 841
1
vote
1
answer
165
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Some questions on partial pseudo anosov maps
Let $S$ be an orientable closed 2-surface with genus at least 2 and $C$ be a non-separating essential simple closed curve in $S$. Denote $S_{C}=S-N(C)$. Let $f$ be a pseudo anosov map of $S_{C}$. Hen …
- 841
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2
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333
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faraway curves in surface
Let $S$ be a compact orientable 2-surface with $\chi(X)\leq -3$. Y.Minsky and H.Masur proved that the curve complex of $X$ is $\delta$-hyperbolic and infinite.
E.Klarreich (see also U.Hamenstadt) prov …
- 841
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2
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341
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The action of periodic map on the complex of curves
Hi, everyone.
Assume $S$ is a genus at least 2 orientable closed surface. And there is a simplical complex
defined on $S$ called Curve complex.
It is well known that any automorphism of surface $ …
- 841
2
votes
1
answer
204
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the carrier graph and Heegaard surface
Let $M$ be orientable 3-manifold admitting a Heegaard splitting $V\cup_{S}W$.
Let $X$ be a carrier graph of $M$ such that rank($X$)=rank($\pi_{1} M$).
Note: A connected graph is called a carrier gr …
- 841
8
votes
2
answers
666
views
Pseudo-Anosov map, Heegaard splitting, hyperbolic 3-manfold
Hi, I am interested in the relationship between the pseudo-anosov map and volume of the hyperbolic 3-manifold.
Assume $H_{1}$ and $H_{2}$ are two handlebodies with $\partial H_{1}=\partial H_{2}=S$. …
- 841
2
votes
1
answer
218
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Requiring references
Assume $V$ be a genus larger than 1 handlebody, $S=\partial_{+} V$.
Denote $N$ be the normal closure of $MCG(V)$ in $MCG(S)$.
Is there any material related to the quotient group $MCG(S)/N$ ?
Thanks! …
- 841
3
votes
2
answers
342
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A question on (1,1) bridge Knot
Hi, everyone. I am interested in the complement of (1,1) bridge knot in a lens space, $S^{3}$. Is there one (1,1) bridge knot in $S^{3}$ or lens space such that its complement is
hyperbolic?
Note …
- 841
5
votes
1
answer
746
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sufficient conditions on Non-Haken manifolds
Is there an algorithm to detect the Non-Haken Manifold?
Or, is there a sufficient condition for a manifold to be
a non-Haken manifold? (off course, I hope that condition is not the ones in its
def …
- 841
6
votes
2
answers
286
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The action of torsion of $MCG(S)$ on curve complex
Hi everyone.
Let $S$ be a closed surface with genus at least 3, $\alpha, \beta$ be the two vertices of
curve complex of $S$ such that $d_{\mathcal {C}(S)}(\alpha, \beta)\geq 3$.
My question is
…
- 841
4
votes
0
answers
137
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Is the mapping class group of a high distance general Heegaard splitting finitely generated?
Let $H_{1}$ and $H_{2}$ are two handlebodies. If $\partial H_{1}$ and $\partial H_{2}$ are homeomorphic, then $H_{1}\cup_{f} H_{2}$ is a Heegaard splitting. To a general Heegaard splitting, one of $H_ …
- 841
1
vote
1
answer
112
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The diameter of the projection of a convex core
Let $M$ be a closed hyperbolic 3-manifold and $H_{g}$ a genus g handlebody. Assume that $\pi: int(H_{g})\rightarrow M$ is a cover. Denote $N\subset H_{g}$ the convex core.
My question is: If the diam …
- 841
4
votes
2
answers
578
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a question on rank of fundamental group
Assume $G$ be the fundamental group of a closed orientable hyperbolic 3-manifold. Let
$G_{1} = \langle a_{1},...,a_{k} \rangle$ be a free subgroup of $G$, and let $G_{2}=\langle a_{k+1} \rangle$ be a …
- 841
4
votes
1
answer
143
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the local structure of an immersed incompressible surface
Assume that $M$ is a closed, irreducible, orientable 3-manifold. Suppose that we have a closed, immersed, incompressible surface $F$ of genus at least 1. Since we only required $F$ to be immersed in $ …
- 841
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Is there a way to classify incompressible surfaces in $\Sigma \times [0,1]$ ?
Please check this paper--http://comp.uark.edu/~yoav/kobayashi-qiu-wang.pdf.
In Proposition 1, they have proved that there are infinitely many incompressible surface based on a simple curve. So I gu …
- 841