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June 10, 2017

Further on

Filed under: clarification of demonstration — Rob @ 3:31 pm

1. Instead of changing to l*l space before creating the joining, we can also change to it as we flatten the crossings. There can be a two to two map from two locations in 3 space to two locations together at an l*l plane. Also we can consider an entire diagram. Diagrams 4 and 5. I use the double crossing loop as an example.
2.This creates a new joining type Z(n) n=1,2,3..
3.The advantage of doing this is that now we can say that we are at the level l*l but we can take advantage of the way movements of points around the double self-intersecting loop are defined in l. Since points and locations are both zero dimensional.
We can have a type of movement of locations 1+ and 1- around the loop while the locations 2+ and 2- at Z(2) stay fixed. Locations move through locations.
4. In particular I can separate Z(1) into 1+, 1- and D(1) while keeping Z(2) as is. Diagram 6.
5. 1+ and 1- can then move through Z(2).

Clarification

Filed under: clarification of demonstration — Rob @ 3:30 pm

1. Start with a crossing in regular 3 space. Diagram 1.
2. By “freezing” the crossing in regular space (the dotted lines) we can then move the crossing to l*l (location of location) space. The locations still cross, one over the other. Diagram 2.
3. We can move the two strands of the crossing to intersect at the “joining” D. Here at the vertex at the location of the locations, we have the two locations. We know which location is associated with which strand of the crossing. Diagram 3. 1+ and 1- represent two parts of the original crossing.

May 27, 2017

Page 1

Filed under: clarification of demonstration — Rob @ 1:18 pm

If we “freeze” the knot in usual space then we can move it in l*l space.

Page 2

Filed under: clarification of demonstration — Rob @ 1:17 pm

There are new crossing types. I can have two other deeper types of diagrams.

Page 3

Filed under: clarification of demonstration — Rob @ 1:14 pm

This is the creation of Z joining. If we have a crossing in l and a crossing in l*l then we can have a Z joining. If we don’t have a crossing in l but do have one in l*l we have a Q joining.

Page 4

Filed under: clarification of demonstration — Rob @ 1:13 pm

This is the description of a D joining coming from a Z joining.

May 22, 2017

Filed under: edited notes on math theory demonstration — Rob @ 4:19 pm

May 16, 2017

Filed under: edited notes on math theory demonstration — Rob @ 11:23 am

I thought it might be simpler to access the third level l*l*l then the alpha and beta parts could separate out. Then there would be three levels. Since we don’t label anymore once we reach the circular form, it must be that there is only a rearrangement of the elements which leads to the two different representations.

May 13, 2017

Filed under: edited notes on math theory demonstration — Rob @ 2:01 pm

May 11, 2017

Filed under: edited notes on math theory demonstration — Rob @ 7:51 pm

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