Surface-Knots in 4-Space by Seiichi Kamada

Author:Seiichi Kamada
Language: eng
Format: epub
Publisher: Springer Singapore, Singapore

Proof

Put . This is a diagram of with respect to the projection of to the xzt-space. Changing the t- and y-coordinates, we obtain D.

Figure 6.1 (Left) shows a diagram of a tangle k of a trefoil knot, and Fig. 6.1 (Right) is a part of a diagram obtained by spinning. By spinning each arc we obtain a sheet of a diagram of .

Fig. 6.1A diagram of a spun trefoil

Now we consider a motion picture of . Let be a diagram in the xzt-space. By considering slices of along planes orthogonal to the t-axis, we have a one-parameter family of diagrams in the xz-plane of cross-sections of F.

Let k be a tangle in . The spinning construction is also understood as follows: Regard as the boundary of , i.e.,

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.