Splicing and the 𝑆𝐿₂(ℂ) Casson invariant

Boden, Hans; Curtis, Cynthia

doi:10.1090/S0002-9939-08-09233-2

Splicing and the $SL_2({\mathbb C})$ Casson invariant
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by Hans U. Boden and Cynthia L. Curtis

Proc. Amer. Math. Soc. 136 (2008), 2615-2623

DOI: https://doi.org/10.1090/S0002-9939-08-09233-2

Published electronically: March 14, 2008

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Abstract:

We establish a formula for the $SL_2({\mathbb C})$ Casson invariant of spliced sums of homology spheres along knots. Along the way, we show that the $SL_2({\mathbb C})$ Casson invariant vanishes for spliced sums along knots in $S^3$.

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