Symmetric unions have been defined as generalizations of Kinoshita-Terasaka's
construction in 1957. They are given by diagrams which look like the connected
sum of a knot and its mirror image with additional twist tangles inserted near
the symmetry axis. Because all symmetric unions are ribbon knots, we can ask
how big a subfamily of ribbon knots they form. It is known that all 21 ribbon
knots with crossing number less or equal 10 are symmetric unions.
In this talk we extend our knowledge about symmetric unions: we prove that
the family of symmetric unions contains all known 2-bridge ribbon knots. The
question, however, whether the three families of 2-bridge ribbon knots, found
by Casson and Gordon in 1974, are a complete list of all 2-bridge ribbon knots,
is still open.Comment: 13 pages (notes for a talk at the Joint Meeting of AMS and DMV at
Mainz, 2005-06-18