An Extension of Casson's Invariant. (AM-126), Volume 126

This monograph describes an invariant, lambda, of oriented rational homology 3-spheres, which is a generalization of Andrew Casson's work in the integer homology sphere case.

A formula describing how lambda transforms under Dehn surgery is provided.

The formula involves Alexander polynomials and Dedekind sums, and can be used to give a rather elementary proof of the existence of lambda.

It is also shown that when M is a Z2-homology sphere, lambda (M) determines the Rochlin invariant of M.