All Questions
8 questions with no upvoted or accepted answers
8
votes
0
answers
298
views
A conjecture about homotopy $S^1\times B^3$'s
$\textbf{Conjecture}:$
Let $X^4$ be a homotopy $S^1\times B^3$ with the following properties:
Attaching a four dimensional 2-handle gives a standard $B^4$.
The $k$-fold cyclic cover is diffeomorphic ...
7
votes
0
answers
1k
views
Applications of E8 manifold
The $E_8$ Cartan matrix is given by,
$$
K_{E_8}=\begin{pmatrix}
2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 \\
-1 & 2 & -1& 0 & 0 & 0 & 0 & 0 \\
...
- 10.5k
6
votes
0
answers
181
views
Kirby diagram of Enriques surface (as the "(1/2) K3 surface")
Not to be confused with $E(1)\cong\mathbb{C}P^2\#9\overline{\mathbb{C}P^2}$, which is also known as a $\frac{1}{2}K3$ surface (in the sense that removing a neighbourhood of a regular torus fiber in $E(...
- 159
5
votes
0
answers
610
views
Closed 4-manifolds with uncountably many differentiable structures
I know that $\mathbb{R}^4$ admits uncountably many differentiable structures. So, I wonder what happens if we consider closed 4-manifolds. Are there any closed 4-manifolds with uncountably many ...
- 683
4
votes
0
answers
128
views
Involutions on $D^4$ with a fixed arc
By a theorem of Livesay, the 3-sphere has a unique (up to equivariant diffeomorphism) smooth involution with exactly two fixed points. Thinking of $S^3$ as the unit sphere in $\mathbb{R}^4$, this ...
4
votes
0
answers
348
views
Smoothability of open 4-manifolds
F. Quinn proved that any open topological 4-manifold admits a smooth structure in Ends of maps III: dimensions 4 and 5.
He first proves the generalized annulus conjecture:
Suppose $h:D^j\times \...
- 91
2
votes
0
answers
197
views
$4$-manifolds with boundary homotopic to $K(G,1)$
I am not very conversant with the $3$-manifold or $4$-manifold theory. The literature I found so far related to $3$-manifold tells me that $S^1\times S^2$ is "very special". It is prime but ...
- 1,177
2
votes
0
answers
95
views
If a Compact $n$-Manifold Immerses in $\mathbb{R}^{n+1}$ is there a Locally Flat Immersion?
Suppose that $M$ is a compact, topological $n$-manifold and there is a topological immersion (i.e. local embedding) of $M$ into $\mathbb{R}^{n+1}$. Is there necessarily a locally flat immersion of $M$...
- 439