Borromean surgery formula for the Casson invariant
Geometric Topology
2010-02-09 v3
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.
Keywords
Cite
@article{arxiv.math/0509335,
title = {Borromean surgery formula for the Casson invariant},
author = {Jean-Baptiste Meilhan},
journal= {arXiv preprint arXiv:math/0509335},
year = {2010}
}
Comments
Final version. 11 pages. To appear in Algebraic & Geometric Topology