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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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(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.

Keywords
gauge theory, spectral flow, Maslov index, spliced sum, torus knot
Mathematical Subject Classification 2000
Primary: 58J30
Secondary: 57M27, 57R57
References
Publication
Received: 8 April 2008
Revised: 1 April 2009
Accepted: 5 April 2009
Published: 5 May 2009
Authors
Hans U Boden
Department of Mathematics and Statistics
McMaster University
1280 Main St W
Hamilton L8S-4K1
Canada
http://www.math.mcmaster.ca/boden
Benjamin Himpel
Mathematisches Institut
Rheinische Friedrich-Wilhelms-Universität Bonn
Beringstr 6
D-53115 Bonn
Germany
http://www.math.uni-bonn.de/people/himpel