Timeline for When can a generalized connected sum be aspherical
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 19 at 19:06 | comment | added | Danny Ruberman | I was referring to the description of the universal cover of the union. This is independent of dimension. | |
| Jul 19 at 0:13 | comment | added | Jeremy | If I'm not mistaken, Cappell’s paper discusses codimension $1$ case in the introduction, and the theorems are for dimensions $\ge 5$. I have $4$-manifolds with codimension $2$ submanifolds! | |
| Jul 18 at 14:02 | comment | added | Danny Ruberman | It’s not hard to describe the universal cover of your manifold in terms of covers of $M-S$ and $N-S$; you can then try to compute the homology of the universal cover and decide if it’s contractible. See for instance the introductory parts of Cappell’s paper on the splitting theorem or papers of Plotnick and Suciu from the 80s. | |
| Jul 18 at 4:50 | comment | added | Jeremy | I understand, thank you. However, if $M$ is a general $T^2$-bundle over $S^2$ that is not necessarily trivial and $S$ and $N$ are the same as above, then can something be said about the asphericity of $M\#_S N$, noting that perhaps $\pi_1(M\#_S N) = \mathbb{Z}^4$ again? | |
| Jul 18 at 2:23 | history | answered | Danny Ruberman | CC BY-SA 4.0 |