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August 13, 2026Open Access

Sheaf-Theoretic Obstructions in Higher Dimensions and Topological Rigidity in the Affine Plane

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Authors

JBJasmine S. Burns

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Overview

This randomized trial uncovers topological obstructions preventing polynomial inverses in higher dimensions, indicating structural limits in affine algebraic geometry.

Key Points

  • The research evaluates the Keller Jacobian conjecture, revealing obstructions in higher dimensions.
  • Identified sheaf-theoretic obstructions for dimensions n ≥ 3.
  • Utilized Čech cohomology to analyze local and global inverses.
  • Constructed examples of counterexamples in infinite moduli spaces.
  • Established that non-zero constant Jacobian mappings lack global inverses for n ≥ 3.
  • Proved n = 2 allows local analytic inverses but not global due to topological rigidity.
  • Provided a lower bound on rational inversions in the BSS complexity model.

Cite This Study

Jasmine S. Burns (2026) studied this question.

synapsesocial.com/papers/6a7d76aa2b0e0cff3f640336https://doi.org/10.5281/zenodo.21893539
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