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arXiv · 2010.14483

Free noncommutative principal divisors and commutativity of the tracial fundamental group

J. E. Pascoe
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Abstract

We define the principal divisor of a free noncommuatative function. We use these divisors to compare the determinantal singularity sets of free noncommutative functions. We show that the divisor of a noncommutative rational function is the difference of two polynomial divisors. We formulate a nontrivial theory of cohomology, fundamental groups and covering spaces for tracial free functions. We show that the natural fundamental group arising from analytic continuation for tracial free functions is a direct sum of copies of $\mathbb{Q}$. Our results contrast the classical case, where the analogous groups may not be abelian, and the free case, where free universal monodromy implies such notions would be trivial.

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BibTeXRIS

J. E. Pascoe. 2020-10-27. Free noncommutative principal divisors and commutativity of the tracial fundamental group. https://arxiv.org/abs/2010.14483

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