# Borromean surgery formula for the Casson invariant

Research paper by Jean-Baptiste Meilhan

Indexed on: 22 Apr '08Published on: 22 Apr '08Published in: Mathematics - Geometric Topology

#### 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, which involves an additional cubic expression in some linking numbers of the surgery link.