论文标题
重言式班级的四个manifolds
Tautological classes of definite 4-manifolds
论文作者
论文摘要
我们证明了对对角定理的重言式或广义的米勒 - 莫里塔·穆尔福德类别，紧凑，光滑，简单地连接的确定性$ 4 $ - manifolds。可以将我们的结果视为唐纳森对角定理的家庭版本。我们使用家庭版本的bauer-furuta共同体精致理论证明了我们的结果。我们利用主要结果来推断有关这种$ 4 $ manifolds的重言式类别的各种结果。特别是，我们完全确定$ \ Mathbb {cp}^2 $和$ \ mathbb {cp}^2 \＃\ Mathbb {cp}^2 $的重言式环。我们还在重言式戒指中得出了一系列线性关系，从某种意义上说，它们具有所有紧凑，平滑，简单地连接的确定$ 4 $ manifolds。
We prove a diagonalisation theorem for the tautological, or generalised Miller-Morita-Mumford classes of compact, smooth, simply-connected definite $4$-manifolds. Our result can be thought of as a families version of Donaldson's diagonalisation theorem. We prove our result using a families version of the Bauer-Furuta cohomotopy refinement of Seiberg-Witten theory. We use our main result to deduce various results concerning the tautological classes of such $4$-manifolds. In particular, we completely determine the tautological rings of $\mathbb{CP}^2$ and $\mathbb{CP}^2 \# \mathbb{CP}^2$. We also derive a series of linear relations in the tautological ring which are universal in the sense that they hold for all compact, smooth, simply-connected definite $4$-manifolds.
