Timeline for Hyperbolic homology spheres with infinite $\mathrm{SL}_2(\mathbb{C})$ character variety
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 17, 2023 at 12:27 | comment | added | Toffee | Yes, you do want it null-homotopic for the extension, and I agree in retrospect this is dodgy for a splicing. | |
| Mar 17, 2023 at 4:38 | comment | added | Danny Ruberman | @HJRW One construction of a degree one map comes from invertible homology cobordisms. I constructed such cobordisms and maps in an old paper, Seifert surfaces of knots in $S^4$. Pacific J. Math. 145 (1990), no. 1, 97–116. | |
| Mar 17, 2023 at 4:35 | comment | added | Danny Ruberman | @Toffee I don't see why the Dehn filled manifold admits a degree one map to the original manifold. You'd have to know that the map on the complement of your hyperbolic knot extends over the torus you glue in. If the knot is null-homotopic, there is an obstruction theory argument for this. But I don't see why there would be a null homotopic curve with that property. | |
| Mar 16, 2023 at 15:20 | vote | accept | Renaud Detcherry | ||
| Mar 16, 2023 at 12:50 | comment | added | Toffee | Drill out a curve so the complement is hyperbolic, then do a hyperbolic Dehn filling. The filled manifold admits a degree $1$ map to $S(K, K^\prime)$. | |
| Mar 16, 2023 at 9:55 | comment | added | HJRW | Could you provide a reference for the construction of the hyperbolic homology sphere that $\pi_1$-surjects the spliced manifold? | |
| Mar 16, 2023 at 0:03 | history | answered | Danny Ruberman | CC BY-SA 4.0 |