The Structure and Enumeration of Link Projections

Martin Bridgeman

MSRI #1995-007

We define a decomposition of link projections whose pieces we
call atoroidal graphs. We describe a surgery operation on 
these graphs and show that all atoroidal graphs can be generated 
by performing surgery repeatedly on  a family of well known link 
projections. This gives a method of enumerating atoroidal 
graphs and hence link projections by recomposing the 
pieces of the decomposition.