Algebraic & Geometric Topology

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

Hans U Boden and Benjamin Himpel

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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
Received: 8 April 2008
Revised: 1 April 2009
Accepted: 5 April 2009
First available in Project Euclid: 20 December 2017

Permanent link to this document
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

Subjects
Primary: 58J30: Spectral flows
Secondary: 57M27: Invariants of knots and 3-manifolds 57R57: Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants [See also 58-XX]

Keywords
gauge theory spectral flow Maslov index spliced sum torus knot

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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