Timeline for Detecting a "bad map" in Fintushel-Stern knot surgery
Current License: CC BY-SA 4.0
3 events
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| Nov 14, 2023 at 20:43 | comment | added | Marco Golla | I think this cannot be true in general, e.g. if $K$ is the unknot and the torus we're removing is a fibre of a Lefschetz fibration. I'm not sure what to expect in the generic case, though. Any experts here care to chime in? | |
| Nov 14, 2023 at 4:10 | comment | added | rab | Thanks for the answer Marco, to follow up then: suppose we do perform the gluing by just any arbitrary map $f:T^3\to T^3$, if it has already been shown that in the case that the "carefully chosen map" $\varphi$ (i.e. the one we know preserves the homology class, etc.), gives an exotic structure, is it at all reasonable to assume that the $X_K$ we get by using the "random" $f$ map also gives rise to an exotic structure? | |
| Nov 14, 2023 at 1:05 | history | answered | Marco Golla | CC BY-SA 4.0 |