Borromean surgery formula for the Casson invariant
  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. 
Jean-Baptiste Meilhan