Volume 8, issue 2 (2008)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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 S3 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