Algebraic & Geometric Topology

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

Hans U Boden and Benjamin Himpel

Full-text: Open access

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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