#### Volume 8, issue 2 (2008)

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Borromean surgery formula for the Casson invariant

### Jean-Baptiste Meilhan

Algebraic & Geometric Topology 8 (2008) 787–801
##### 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.

##### Keywords
Casson invariant, Borromean surgery, finite type invariants
##### Mathematical Subject Classification 2000
Primary: 57N10, 57M27