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
Abstract

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

Keywords
gauge theory, spectral flow, Maslov index, spliced sum, torus knot
Mathematical Subject Classification 2000
Primary: 58J30
Secondary: 57M27, 57R57