All Questions
Tagged with 3-manifolds gt.geometric-topology
65 questions with no upvoted or accepted answers
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Existence of smooth structures on topological $3$-manifolds with boundary
It is said in this thread Unique smooth structure on $3$-manifolds that every topological $3$-manifold admits a smooth structure. However it is not specified whether the manifolds are allowed to have ...
- 21
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124
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Non Seifert incompressible surfaces detected by ideal points
Given a 3-manifold with toric boundary, the Culler-Shalen theory associates an incompressible surface to any ideal point of its character variety. From the proof of the Neuwirth conjecture, one knows ...
- 223
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contact structure on double branched covers of $S^3$
We can assign a natural contact structure to double branched cover of a transverse knot $k$ in the $3$-sphere with its standard contact structure $(S^3,\xi_{st})$, as described in:http://arxiv.org/pdf/...
- 1,335
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Extend a circle action on $3$-manifolds
Let $M$ be an oriented closed $3$-manifold equipped with an effective smooth circle action.
Can we have a classification of all such $M$ such that there exists a $4$-manifold $N$ with $\partial N=M$, ...
- 891
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215
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Circle-valued Morse function and minimal genus
I think the following two statements are true, and most likely are in the literature. If so, could someone point me to some references? If not, counterexamples?
Let $Y$ be a closed oriented connected ...
- 11
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129
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Open cone homeomorphic to the Euclidean space
Let $X$ be a topological space and the open cone $C(X)$ over $X$ is defined to be $X \times [0,1)$ with $X \times \{0\}$ identified. Suppose $C(X)$ is homeomorphic to $\mathbb R^4$, can we prove that $...
- 2,535
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Do different decompositions of Dehn twists induce the same cobordisms between mapping tori?
Suppose $Y=T^2\times I/f$ is a mapping torus, where $f$ is a diffeomorphism of $T^2$. Suppose $c$ is a curve on $T^2\times \{1\}$ with surface framing and suppose $D_c$ is the positive Dehn twist ...
- 673
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297
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Boundary map in Mayer-Vietoris sequence of cohomology
Suppose $M$ is a 3-manifold with connected boundary. Let $T$ be a tangle in $M$, i.e., $T$ is a embedded connected 1-submanifold whose boundary is on $\partial M$ ($T$ is not closed). Moreover, ...
- 673
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References on Hyperbolic Geometry and Teichmuller Theory
I am asking a soft question here.
I am learning hyperbolic geometry on my own. Recently, I have completed the book "Fuchsian Groups" by Svetlana Katok. Also, I have background in Lee's three ...
user318929
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Covers of a 4-manifold pull back a cohomology class to any algebraic multiple
Fix an algebraic integer $x\neq 0$. Is there a closed smooth 4-manifold $M$ with a class $\rho\in H^{1}_{\mathrm {dR} }(M)$ and a smooth covering map $\phi:M\to M$ such that $\phi^*\rho=x\rho$?
Is ...
user164740
1
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224
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Embedded surfaces in pseudo-Anosov mapping tori
Given a genus $g$ (where $g \geq 2$) closed surface $S$, and a pseudo-Anosov map $\varphi: S \to S$, one can construct the mapping torus, which turns out to be a hyperbolic $3$-manifold, which we'll ...
- 289
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211
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Toral decomposition
I have a couple of questions on the following theorem:
Theorem. (Jaco, Shalen)
Let $M$ be a compact, irreducible, orientable 3-manifold with incompressible boundary. There exists a collection $\...
- 43
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Bipartedly slice links and their surgeries
A link L in $S^3$ is said to be strongly slice if $L=∂D$,where $D$ is a disjoint union of smoothly and properly embedded disks in $B^4$.
A link $L$ in $S^3$ is called bipartedly slice if $L = L_1 \cup ...
user160180
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129
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Open Book Decompositions of M^3's : Finding the Projection Map (Hope in Coordinates) in an Abstract Open Book
all:
I want to know how to find out , hopefully in coordinates, (but I'll take what's available) , the description of the projection map in an abstract open-book decomposition.
Open book ...
- 1
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contact structure on 3 manifolds
every orientable closed 3-manifold admits a contact structure. how we can construct this contact structure? if the manifold is prime what will happen?
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