Volume 9, issue 2 (2009)

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Splitting the spectral flow and the $\mathrm{SU}(3)$ Casson invariant for spliced sums

Hans U Boden and Benjamin Himpel

Algebraic & Geometric Topology 9 (2009) 865–902

We show that the SU(3) Casson invariant for spliced sums along certain torus knots equals 16 times the product of their SU(2) Casson knot invariants. The key step is a splitting formula for su(n) spectral flow for closed 3–manifolds split along a torus.

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gauge theory, spectral flow, Maslov index, spliced sum, torus knot
Mathematical Subject Classification 2000
Primary: 58J30
Secondary: 57M27, 57R57
Received: 8 April 2008
Revised: 1 April 2009
Accepted: 5 April 2009
Published: 5 May 2009
Hans U Boden
Department of Mathematics and Statistics
McMaster University
1280 Main St W
Hamilton L8S-4K1
Benjamin Himpel
Mathematisches Institut
Rheinische Friedrich-Wilhelms-Universität Bonn
Beringstr 6
D-53115 Bonn