Algebraic & Geometric Topology

Borromean surgery formula for the Casson invariant

Jean-Baptiste Meilhan

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

Permanent link to this document
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

Subjects
Primary: 57N10: Topology of general 3-manifolds [See also 57Mxx] 57M27: Invariants of knots and 3-manifolds

Keywords
Casson invariant Borromean surgery finite type invariants

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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