论文标题
复杂的恢复性与相关和几何取向
Complex cobordism with involutions and geometric orientations
论文作者
论文摘要
我们计算了COBORDISM环$ω^{C_2} _*稳定的复杂歧管，并调查代表它的$ C_2 $ -Spectrum $ω_{C_2} $。我们介绍了以几何为导向的$ C_2 $ -Spectrum的概念，该概念扩展了一个复杂的面向$ C_2 $ -SPECTRUM的概念，其中$ω__{C_2} $是通用示例。示例，除了$ω_{C_2} $之外，还包括Eilenberg-Maclane Spectrum $ H \下划线{\ Mathbb {Z}} _ {C_2} $和Connective Cover $ k_ {C_2} $ $ C_2} $ $ C_2 $ equivariant $ k $ k $ - $ - $ - $ - $ - $ - $ - $ - $ - $ - $ - $ - $。在代数方面，我们定义和研究过滤了$ c_2 $ equivariant正式组法，这是由几何定向$ C_2 $ -SPECTRA确定的代数结构。我们证明了已过滤的$ C_2 $ Equivariant正式集团法律的一些基本属性，以及过滤的$ C_2 $ equivariant正式组定律，由$ω__{C_2} $确定。
We calculate the cobordism ring $Ω^{C_2}_*$ of stably almost complex manifolds with involution, and investigate the $C_2$-spectrum $Ω_{C_2}$ which represents it. We introduce the notion of a geometrically oriented $C_2$-spectrum, which extends the notion of a complex oriented $C_2$-spectrum, and of which $Ω_{C_2}$ is the universal example. Examples, in addition to $Ω_{C_2}$, include the Eilenberg-Maclane spectrum $H \underline{\mathbb{Z}}_{C_2}$ and the connective cover $k_{C_2}$ of $C_2$-equivariant $K$-theory. On the algebraic side, we define and study filtered $C_2$-equivariant formal group laws, which are the algebraic structures determined by geometrically oriented $C_2$-spectra. We prove some of the fundamental properties of filtered $C_2$-equivariant formal group laws, as well as a universality statement for the filtered $C_2$-equivariant formal group law determined by $Ω_{C_2}$.
