Abstract:
We introduce the equivalence relation ρ on the
set of Carter diagrams and construct an explicit transformation of
any Carter diagram containing l-cycles with l > 4 to an equivalent
Carter diagram containing only 4-cycles. Transforming one Carter
diagram Γ1 to another Carter diagram Γ2 we can get a certain
intermediate diagram Γ′ which is not necessarily a Carter diagram.
Such an intermediate diagram is called a connection diagram. The
relation ρ is the equivalence relation on the set of Carter diagrams
and connection diagrams. The properties of connection and Carter
diagrams are studied in this paper. The paper contains an alternative
proof of Carter’s classification of admissible diagrams.
