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Preprint
Free noncommutative principal divisors and commutativity of the tracial fundamental group
arXiv (Cornell University)
27 Oct 2020
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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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