Abstract

We describe the structure of the coefficient ring \(W^*(pt)=\varOmega_W^*\) of the \(c_1\)-spherical bordism theory for an arbitrary \(SU\)-bilinear multiplication. We prove that for any \(SU\)-bilinear multiplication the formal group of the theory \(W^*\) is Landweber exact. Also we show that after inverting the set \(\mathcal{P}\) of Fermat primes there exists a complex orientation of the localized theory \(W^*[\mathcal{P}^{-1}]\) such that the coefficients of the corresponding formal group law generate the whole coefficient ring \(\varOmega_W^*[\mathcal{P}^{-1}]\).

中文翻译：

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$$c_1$$ 中形式群律的 Landweber 精确性 -Spherical Bordism

摘要

我们描述了任意\(SU\ ) 双线性乘法的\(c_1\) -球面棱镜理论的系数环\(W^*(pt)=\varOmega_W^*\)的结构。我们证明对于任何\(SU\)双线性乘法，理论\(W^*\)的形式群是 Landweber 精确的。我们还表明，在反转费马素数集合\(\mathcal{P}\)后，存在局域理论\(W^*[\mathcal{P}^{-1}]\) 的复方向，使得相应的形式群律的系数生成整个系数环\(\varOmega_W^*[\mathcal{P}^{-1}]\)。