4-plats

How to create figures and illustrations for knot theory papers

4-plats

Postby mousa on Mon Oct 19, 2009 6:42 pm

how do I create 4-plats? i see that under Cons one can create braids using the character notation. i'd like to create 4-plats using the Conway notation, is that possible? for example, how to I create <1,4,1>?
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Re: 4-plats

Postby rob on Mon Oct 19, 2009 6:55 pm

mousa wrote:how do I create 4-plats? i see that under Cons one can create braids using the character notation. i'd like to create 4-plats using the Conway notation, is that possible? for example, how to I create <1,4,1>?


use the conway command, in your example, you'd use

conway 141

you might want to fiddle with the tg1offset parameter to get different effects.
for example, try

tg1offset = 3
conway 141
go 15


the go command is just to smooth the embedding to get a nicer knot

note that the conway command will print the equivalent tangle command string.
in this case conway 141 is equivalent to the command tangle 14*1*

be sure to read about the tangle calculator by clicking on the help button when on the tangle calculator control panel.

note that although the manual at http://knotplot.com/manual/commands.html#conway says that only rational knots are possible with the conway command, this is no longer the case. you can enter, for example, and of the following:

conway 3,4,3,5
conway 8*
conway 21,21,2
conway .2.20

the complete Conway notation is supported. to easily see what's possible, run the tangles demo in the Knot theory section of the DemoA control panel in KnotPlot.
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