## Algebraic & Geometric Topology

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

#### Abstract

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.

#### Article information

Source
Algebr. Geom. Topol., Volume 9, Number 2 (2009), 865-902.

Dates
Revised: 1 April 2009
Accepted: 5 April 2009
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.agt/1513797004

Digital Object Identifier
doi:10.2140/agt.2009.9.865

Mathematical Reviews number (MathSciNet)
MR2505128

Zentralblatt MATH identifier
1180.57019

#### Citation

Boden, Hans U; Himpel, Benjamin. Splitting the spectral flow and the $\mathrm{SU}(3)$ Casson invariant for spliced sums. Algebr. Geom. Topol. 9 (2009), no. 2, 865--902. doi:10.2140/agt.2009.9.865. https://projecteuclid.org/euclid.agt/1513797004

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