# connected sum

## Primary tabs

Synonym:
knot sum
Type of Math Object:
Definition
Major Section:
Reference
Groups audience:

## Mathematics Subject Classification

### Connected sum graphics

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.

### Re: Connected sum graphics

You might look at
http://www.dpmms.cam.ac.uk/~al366/xytutorial.html
for examples of drawing knots with xypic.

Roger

### Re: Connected sum graphics

That all looks very nice. In the graphics sandbox I tried the second diagram from http://www.dpmms.cam.ac.uk/~al366/braidtutorial/Knots.html 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).

### Re: Connected sum graphics

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

### Re: Connected sum graphics

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.

### Lie superalgebras

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.

Regards,

Halfamatician