论文标题
奇学基本组的免费非交易性主要分区和通勤性
Free noncommutative principal divisors and commutativity of the tracial fundamental group
论文作者
论文摘要
我们定义了自由非交易函数的主要除数。我们使用这些除数比较自由非交通函数的确定性奇异性集。我们表明，非交通合理函数的除数是两个多项式除数的差异。 我们制定了一个非平凡的统一理论，基本群体和涵盖了奇特自由功能的空间。我们表明，由奇特自由功能的分析延续引起的自然基础群体是$ \ mathbb {q} $的直接副本。我们的结果与经典案例进行了对比，在古典情况下，类似群体可能不是Abelian，而自由的普遍单构型意味着这种概念是微不足道的。
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.
