Timeline for Trefoil knot and Figure 8 knot are prime knots
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 20, 2014 at 15:21 | vote | accept | Haikal Yeo | ||
| May 3, 2013 at 18:43 | comment | added | Dan Rust | I used Wikipedia's definition of genus=(2 + #crossings - #seifert_circles - #knot_components)/2 If $K$ is a knot, this becomes genus=(1 + #crossings - #seifert_circles)/2. Without drawing a picture I can't really show how I got 3 circles but I guess I got one small circle at the top, and then one big circle with another smaller circle on the inside. That's the best way I can describe it. I can draw a picture if it's still not clear but I would suggest drawing it again for yourself and carefully going through the crossing switches. | |
| May 3, 2013 at 18:29 | comment | added | Haikal Yeo | How do you get 3 Seifert circles for the figure 8 knot? I used the diagram from Wikipedia (which I hope is the standard diagram) and only managed to get 2 - the topmost "hole" and the bottom-middle "hole". Apologies if that wasn't the best descrption. Also, isn't the formula $g(S)=(c-s+1)/2? Where did your number 2 come in? | |
| May 3, 2013 at 13:20 | history | edited | Dan Rust | CC BY-SA 3.0 |
added 33 characters in body
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| May 3, 2013 at 12:31 | history | answered | Dan Rust | CC BY-SA 3.0 |