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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Details
Title
Free noncommutative principal divisors and commutativity of the tracial fundamental group
Creators
J. E Pascoe
Publication Details
arXiv (Cornell University)
Resource Type
Preprint
Language
English
Academic Unit
Mathematics
Other Identifier
991021879759604721
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