All Questions
9 questions
5
votes
1
answer
380
views
Proving the Cork Theorem
I am reading Kirby's paper paper "Akbulut's corks and h-cobordisms of smooth simply connected 4-manifolds" and I have a question about how to actually prove the cork theorem from the results ...
14
votes
0
answers
326
views
When can we extend a diffeomorphism from a surface to its neighborhood as identity?
Let $M$ be a closed and simply-connected 4-manifold and let $f: M^4 \to M^4$ be a diffeomorphism such that $f^*: H^*(M;\mathbb{Z})\to H^*(M;\mathbb{Z})$ is the identity map. Moreover, let $\Sigma \...
- 3,751
4
votes
1
answer
111
views
A neighborhood of a 2-disc $D\subset\Bbb R^4$ that tapers off towards the boundary?
I am given a PL 2-disc $D\subset\Bbb R^4$ (everything PL from here on) and I need a "neighborhood" $N\simeq B^4$ (PL-homeomorphic to a 4-ball) so that $\partial N\cap D=\partial D$.
If I got ...
- 13.6k
8
votes
1
answer
233
views
If $M$ is contractible manifold and $X\subset \partial M$, does the cone over $X$ embed in $M$?
Let $M$ be a compact contractible manifold, $X\subset\partial M$ and $C_X$ the cone over $X$.
Question: Is it true that $C_X$ embeds in $M$ with its boundary $\partial C_X$ mapped to $X\subset \...
- 13.6k
3
votes
0
answers
405
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
7
votes
1
answer
731
views
What is "topology in dimension 3.5"?
I've noticed a couple of conference titles which reference something called
"topology in dimension 3.5," such as this one and this one. This subject seems quite mysterious to me — it looks like ...
- 6,881
7
votes
0
answers
504
views
Intersection form of logarithmic transformations
Now I want to calculate the intersection form of a logarithmic transformation which is defined as follows.
Let $X$ be an oriented, closed, simply-connected 4-manifold and $T^2\subset X$
be an ...
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
6
votes
0
answers
188
views
Quotients of 4-sphere by smooth $Z_p$ actions with knotted fixed point sets
This question is closely related to another I asked today.
Giffen showed in 1966 that the generalized Smith conjecture is false by constructing for odd $p$ a smooth $Z_p$ action on $S^4$ with fixed-...
- 2,851