All Questions
Tagged with surgery-theory 4-manifolds
9 questions
6
votes
1
answer
472
views
4-manifold obtained from a ribbon disk exterior by attaching a 2-handle is simply-connected if its boundary is a homology sphere
I am reading Lemma 2.1 of this paper (https://arxiv.org/pdf/2012.12587.pdf) and I can't see why $W$ is simply-connected. Here is the situation:
Let $K$ be a ribbon knot in $S^3$; it bounds a ribbon ...
- 335
3
votes
0
answers
86
views
Integral homology $S^1\times S^2$'s smoothly bounding integral homology $S^1\times B^3$'s
Suppose we are given a compact orientable 3-manifold $M$ which is an integral homology $S^1\times S^2$. Then is there a way to determine whether $M$ bounds a smooth compact orientable 4-manifold which ...
- 335
2
votes
0
answers
130
views
Attaching a 2-handle to a once-twisted unlink in the boundary of the 4-ball
Consider the 3-sphere $S_3$ with an unlink loop $L$ whose tubular neighborhood is identified with the solid torus $B_2\times S_1$ with one twist, i.e., such that the image of $x\times S_1$ (where $x$ ...
- 3,001
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
3
votes
0
answers
406
views
A user guide to the theory on Corks
I am trying to digest the meanings of the corks from the both:
algebraic topology
and
geometry topology
perspectives.
Studying corks is important for understanding the exotic phenomenon of 4-...
- 10.5k
2
votes
0
answers
123
views
Surgery and Curvature on Foliation
Let $X$ be an oriented closed smooth $4$-manifold. Suppose that $TM$ admits a foliation $\mathcal F$ of dimension two, and admits a positvescalar curvature.
Q: If we do the surgery on $X$ to reduce ...
- 1,915
3
votes
0
answers
104
views
A link of four 2-tori $T^2$ in $S^2 \times S^2$
Step 1: We glue two sets of complement space of $D^2\times T^2$ out of the 4-sphere $S^4$, through their $T^3$ boundary with their three $S^1$ boundaries of $T^3$ cyclic permuted to obtain a new 4-...
- 10.5k
10
votes
2
answers
544
views
Obtain 4-manifolds by repeating surgeries of submanifolds in $S^4$
In his paper QFT and Jones Polynomials, Witten states: "It is a not too deep result that every 3-manifold can be obtained from or reduced to $S^3$ (or any other desired 3-manifold) by repeated ...
- 755
6
votes
0
answers
199
views
Surgering locally flat tori in 4-manifolds
Is there a locally flat torus in some not smoothable topological 4-manifold such that surgering on it produces a smoothable 4-manifold? Surgering means removing a tubular neighborhood and reattaching ...
- 2,283