Demonstrates conditions under which stably free R-modules are free in real smooth affine domains, indicating implications for algebraic topology.
Let R be a real smooth affine domain of dimension 3 such that R has either no real maximal ideals or the intersection of all real maximal ideals in R has height at least 1. Then we prove that all stably free R-modules of rank 2 are free if and only if the Hermitian K-theory group WSL(R) is trivial.
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Tariq Syed (2026) studied this question.
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