Splitting the spectral flow and the SU(3) Casson invariant for spliced sums
Hans U. Boden, Benjamin Himpel
TL;DR
This paper establishes a relationship between the SU(3) Casson invariant of spliced sums along specific torus knots and the product of their SU(2) Casson knot invariants, utilizing a spectral flow splitting formula.
Contribution
It introduces a splitting formula for su(n) spectral flow on closed 3-manifolds split along a torus, linking SU(3) and SU(2) invariants in knot theory.
Findings
SU(3) Casson invariant equals 16 times the product of SU(2) invariants for certain spliced sums.
Derived a spectral flow splitting formula for su(n) on split 3-manifolds.
Established a new connection between SU(3) and SU(2) invariants in knot theory.
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.
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