具有对合和几何定向的复配边
Complex cobordism with involutions and geometric orientations
摘要：
本文计算了稳定殆复流形的配边环$Ω^{C_2}_*$，并研究了它的$C_2$ -谱$Ω_{C_2}$，引入了几何定向$C_2$ -谱的概念，推广了复定向$C_2$-谱的概念，其中$Ω_{C_2}$是它的普遍例子.除了$Ω_{C_2}$之外，实例还包括$K$-等变$C_2$-理论的Eilenberg-Maclane谱$H \underline{\mathbb{Z}}_{C_2}$和连接覆盖$k_{C_2}$。在代数方面，我们定义并研究了过滤$C_2$ -等变形式群律，它是由几何定向的$C_2$ -谱所决定的代数结构。证明了过滤$C_2$ -等变形式群律的一些基本性质，以及由$Ω_{C_2}$确定的过滤$C_2$ -等变形式群律的普适性陈述.
英文摘要：
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 $Ω_{C_2}$.
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