Borromean surgery formula for the casson invariant

Abstract

It is known that every oriented integral homology 3 -sphere can be obtained from S 3 by a finite sequence of Borromean surgeries. We give an explicit formula for the variation of the Casson invariant under such a surgery move. The formula involves simple classical invariants, namely the framing, linking number and Milnor's triple linking number. A more general statement, for n independent Borromean surgeries, is also provided. © 2008 Algebraic & Geometric Topology.