标题： 非光滑卡拉比-丘结构对于代数和余代数 显示英文标题

标题： Nonsmooth Calabi-Yau structures for algebras and coalgebras

摘要： 我们证明了广义Calabi-Yau微分分次(余)代数与广义对称微分分次(余)代数是Koszul对偶的，而不需要假设任何光滑性或有限性假设。 同样地，我们证明了Gorenstein和Frobenius是Koszul对偶的性质。 作为应用，我们给出了Poincaré对偶空间的新特征，该特征将Félix-Halperin-Thomas的一个定理扩展到了非单连通的情形。 显示英文摘要

摘要： We show that generalised Calabi-Yau dg (co)algebras are Koszul dual to generalised symmetric dg (co)algebras, without needing to assume any smoothness or properness hypotheses. Similarly, we show that Gorenstein and Frobenius are Koszul dual properties. As an application, we give a new characterisation of Poincar\'e duality spaces, which extends a theorem of F\'elix- Halperin-Thomas to the non-simply connected setting.