All Questions
9 questions
55
votes
3
answers
6k
views
Kirby calculus and local moves
Every orientable 3-manifold can be obtained from the 3-sphere by doing surgery along a framed link. Kirby's theorem says that the surgery along two framed links gives homeomorphic manifolds if and ...
- 23.5k
25
votes
2
answers
3k
views
Proofs of Kirby's theorem
Each orientable 3-manifold can be obtained by doing surgery along a framed link in the 3-sphere. Kirby's theorem says that two framed links give homeomorphic manifolds if and only if they are obtained ...
- 23.5k
11
votes
2
answers
703
views
Do the results of (1/n)-surgery determine the link?...
Knowing the result of knot surgery is often not enough to determine the knot. Indeed, there are 3-manifolds admitting an infinite number of descriptions as surgery on a (1-component) knot in $S^3$. ...
- 653
8
votes
0
answers
445
views
Integer surgeries along links yielding lens spaces
Does there exist an integer $N$ such that any lens space $L(p,q)$ can be obtained by integer surgery from $S^3$ along a link $L$ with at most $N$ components?
EDIT:
I have worked out the comment by ...
- 1,314
7
votes
2
answers
534
views
Does there exist a Dehn filling of an irreducible 3-manifold with toroidal boundaries which is still irreducible?
Let $M$ be a compact, orientable, irreducible 3-manifold with incompressible toroidal boundary (there might be more than one boundary component). Is it always possible to choose appropriate slopes on ...
- 605
5
votes
1
answer
433
views
Dehn surgery on $S^3$ along a Hopf link with rational surgery coefficients
Is there an exhaustive list of conditions satisfied by rational surgery coefficients assigned to the components of the Hopf link in $S^3$ such that the resulting 3-manifold by Dehn surgery acting on $...
4
votes
0
answers
172
views
Survey or good reference of taut foliations
I am interested in the topology of foliations.
In particular, I want to understand taut foliations, or projectively Anosov flows, and Anosov flows.
I guess that
A. Candel and L. Conlon, Foliations I (...
- 73
2
votes
1
answer
197
views
Two links with the same signatures but unknown if they are related by Kirby moves
I am wondering if there are links $L_1, L_2$ in the sphere $S^3$ such that:
the signatures of $L_1, L_2$ are known.
we do not know if they are related by Kirby moves.
If so, could you specify the ...
user22741
0
votes
0
answers
78
views
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