Superpotential algebras and manifolds

Details Superpotential algebras and manifolds Superpotential algebras and manifolds

2010-10-18

arxiv.org/abs/1010.3564v2

Mathematics

K-Theory and Homology

40 pages, 2 figures, all comments welcome. Thanks to M. Kontsevich, V. Ginzburg, M, Van den Bergh and B. Keller for helpful co

Scientific paper

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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