What question did this study set out to answer?

This research examines an explicit three-dimensional counterexample to the Jacobian Conjecture, focusing on its spectral geometry.

July 26, 2026Open Access

The A₂ Spectral Geometry of the 2026 Jacobian Counterexample

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TRThomas Ruble

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Implication

Research note documents an inverse problem's geometry in a three-dimensional Jacobian counterexample, implying broader implications for mathematical theory.

Key Points

This research examines an explicit three-dimensional counterexample to the Jacobian Conjecture, focusing on its spectral geometry.
Identified an explicit coordinate change near the triple-root curve to connect to A2 singularity
Analyzed the generic inverse cover's S3 monodromy
Studied the pushforward algebra of a three-sheeted cover to define a canonical sl_3(C)-bundle.
Established that the inverse family corresponds to a miniversal deformation of the A2 singularity
Demonstrated the generic inverse cover possesses full S3 monodromy
Classified a canonical bundle comprising root spaces and characteristics of Weyl monodromy.

Cite This Study

Thomas Ruble (2026) studied this question.

synapsesocial.com/papers/6a65a422d3aea3239cd76e33 https://doi.org/10.5281/zenodo.21519096

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Implication

Research note documents an inverse problem's geometry in a three-dimensional Jacobian counterexample, implying broader implications for mathematical theory.

The A₂ Spectral Geometry of the 2026 Jacobian Counterexample

Discussion

Member takes

Implication

Key Points

Cite This Study

The A₂ Spectral Geometry of the 2026 Jacobian Counterexample

Discussion

Member takes

Implication

Key Points

Cite This Study

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