Geodesic
Borromean surgery formula for the Casson invariant
Meilhan, Jean-Baptiste1
1CTQM - Department of Mathematical Sciences, University of Aarhus, Ny Munkegade, bldg 1530, 8000 Aarhus C, Denmark
Algebraic and Geometric Topology, Tome 8 (2008) no. 2, pp. 787-801
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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.

DOI : 10.2140/agt.2008.8.787
Keywords: Casson invariant, Borromean surgery, finite type invariants

Meilhan, Jean-Baptiste  1

1 CTQM - Department of Mathematical Sciences, University of Aarhus, Ny Munkegade, bldg 1530, 8000 Aarhus C, Denmark 
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Meilhan, Jean-Baptiste. Borromean surgery formula for the Casson invariant. Algebraic and Geometric Topology, Tome 8 (2008) no. 2, pp. 787-801. doi: 10.2140/agt.2008.8.787

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