It is known that every oriented integral homology –sphere can be obtained from 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 independent Borromean surgeries, is also provided.
"Borromean surgery formula for the Casson invariant." Algebr. Geom. Topol. 8 (2) 787 - 801, 2008. https://doi.org/10.2140/agt.2008.8.787