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connected sum

knot sum
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After mps's correction to make the knot graphics "prettier" (meaning smoother with no unnecessary cusps) I thought I could just redraw them by hand. Unfortunately, my hands just aren't as steady as they used to be. In exchange for no arthritis pain I pay the price in shakiness and unsteadiness. I hope a young man with drawing skills will pick up this entry and make much better looking graphics. I don't mind if you delete my graphics, though you may want to keep them for reference until you get the better graphics in place.

You might look at
for examples of drawing knots with xypic.


That all looks very nice. In the graphics sandbox I tried the second diagram from I added \usepackage[all, knot]{xy} to the preamble like it says but when I clicked preview I got an unexpected Noosphere error. (The preamble change probably did not stick then).

Did you try just uncommenting the usepackage{xypic} in the standard preamble?

It was already uncommented for something else, which then would mean usepackage[all, knot]{xy} is redundant. I tried again, same helpful unexpected Noosphere error.

Hello, I am a new user. I have been working in signal processing data transform design, currently for applications in geophysics. One of the transform output spaces that I have created is symmetric. The definition that I have (and understand!) for a Lie algebra is as follows:

A non-associative algebra is said to be a Lie algebra if it's multiplication obeys the Lie conditions
1) x squared equals zero and
2) (xy)z+(yz)x+(zx)y=0 (Jacobi Identity)

Given this definition, can anyone add the other conditions that a Lie superalgebra must satisfy, in the same kind of mathematical language? Your definition on the web-site will take me a long time to understand, as I have not read a great deal of abstract algebra.



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