Borromean surgery formula for the Casson invariant

Meilhan, Jean-Baptiste

doi:10.2140/agt.2008.8.787

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Borromean surgery formula for the Casson invariant

Jean-Baptiste Meilhan

Algebraic & Geometric Topology 8 (2008) 787–801

DOI: 10.2140/agt.2008.8.787

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

References

Publication

Received: 5 February 2008

Revised: 3 March 2008

Accepted: 5 March 2008

Published: 25 May 2008

Authors

Jean-Baptiste Meilhan
CTQM - Department of Mathematical Sciences University of Aarhus Ny Munkegade, bldg 1530 8000 Aarhus C Denmark

Volume 8, issue 2 (2008)