Three Important Examples

Boy’s Surface, Gilller’s Surface, and Fox’s Example 12 are among the most important examples of which we know that illustrate problems in embedding surfaces in 4-dimensional space (smoothly and with the standard smooth structures). The talk begins with a discussion of decker sets in general. Constructions of all three surface will be presented in fairly complete ways.
Since these examples are quite well-known (even though I am not sure what we mean by a well-known mathematical example), not a lot of new material will be discussed. On the other hand in my own experience, not so geometrically inclined researcher have troubles with the diagrammatic methodology. So it is my hope that by seeing these examples, these same researchers will become more comfortable with the methods.