## Algebraic & Geometric Topology

### Borromean surgery formula for the Casson invariant

Jean-Baptiste Meilhan

#### 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 8, Number 2 (2008), 787-801.

Dates
Revised: 3 March 2008
Accepted: 5 March 2008
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.agt/1513796844

Digital Object Identifier
doi:10.2140/agt.2008.8.787

Mathematical Reviews number (MathSciNet)
MR2443096

Zentralblatt MATH identifier
1144.57010

#### Citation

Meilhan, Jean-Baptiste. Borromean surgery formula for the Casson invariant. Algebr. Geom. Topol. 8 (2008), no. 2, 787--801. doi:10.2140/agt.2008.8.787. https://projecteuclid.org/euclid.agt/1513796844

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