Splitting the spectral flow and the SU(3) Casson invariant for spliced sums

Boden, Hans U; Himpel, Benjamin

doi:10.2140/agt.2009.9.865

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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

DOI: 10.2140/agt.2009.9.865

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 $s u (n)$ 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

Volume 9, issue 2 (2009)