Applications of the lantern identity

Abstract

The purpose of this note is to unify the role of the lantern identity in the proof of several finiteness theorems. In particular, we show that for every nonnegative integer m, the vector space (over the rationals) of type m (resp. T-type m) invariants of integral homology 3-spheres are finite dimensional. These results have already been obtained by [Oh] and [GL2] respectively; our derivation however is simpler, conceptual and relates to several other applications of the lantern identity.