超势代数与流形
Superpotential algebras and manifolds
摘要：
本文研究一类特殊的Calabi-Yau代数（在Ginzburg意义下）：作为无圈流形的基本群代数而产生的代数。动机部分由“超势描述”motivic唐纳森-托马斯理论的有用性，我们调查的问题，这些代数是否承认超势介绍。我们建立了一个广泛的类的非循环流形，包括所有的双曲流形的基本群代数，不承认这样的描述，反驳金兹伯格的猜想。我们还描述了一类流形，承认这样的描述，并讨论了一点他们的motivic唐纳森-托马斯理论。最后，与拓扑域论的一些联系进行了说明。
英文摘要：
In this paper we study a special class of Calabi-Yau algebras (in the sense of Ginzburg): those arising as the fundamental group algebras of acyclic manifolds. Motivated partly by the usefulness of `superpotential descriptions' in motivic Donaldson-Thomas theory, we investigate the question of whether these algebras admit superpotential presentations. We establish that the fundamental group algebras of a wide class of acyclic manifolds, including all hyperbolic manifolds, do not admit such descriptions, disproving Ginzburg's conjecture regarding them. We also describe a class of manifolds that do admit such descriptions, and discuss a little their motivic Donaldson-Thomas theory. Finally, some links with topological field theory are described.
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