Some Graphics

In here are various graphics which I have made for one reason or another. If they are of use to you, feel free to use them.

Intersecting planes

These slides illustrate the various ways in which planes can intersect in 3-dimensional space. You see here the ways in which the intersection is 0-dimensional (a point) or 1-dimensional.


0-dimensional	1-dimensional

Empty intersection	Empty intersection	Empty intersection

Some Seifert surfaces

A Seifert surface of a knot or link is a surface with boundary the given knot/link. For example, this is a Seifert surface for the trefoil (shown alongside):

A boundary link has a Seifert surface which is a disjoint union of the Seifert surfaces of the 2 components. An example is the following link - here the boundary of each component is a trefoil.

Note that not every link is a boundary link, by a long way: the simplest non-trivial link, the Hopf link is not a boundary link. One Seifert surface for the Hopf link is this:

Please note: this page is very much under development, but should gradually acquire some useful content.