In this paper we identify conditions under which the cohomology $H^*(\OmegaM\xi;\k)$ for the loop space $\Omega M\xi$ of the Thom space $M\xi$ of aspherical fibration $\xi\downarrow B$ can be a polynomial ring. We use theEilenberg-Moore spectral sequence which has a particularly simple form when theEuler class $e(\xi)\in H^n(B;\k)$ vanishes, or equivalently when an orientationclass for the Thom space has trivial square. As a consequence of ourhomological calculations we are able to show that the suspension spectrum$\Sigma^\infty\Omega M\xi$ has a local splitting replacing the James splittingof $\Sigma\Omega M\xi$ when $M\xi$ is a suspension.
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机译：在本文中，我们确定了非球面振动$ \ xi的Thom空间$ M \ xi $的环路空间$ \ Omega M \ xi $的同调$ H ^ *（\ OmegaM \ xi; \ k）$的条件\ downarrow B $可以是一个多项式环。我们使用Eilenberg-Moore光谱序列，当Euler类$ e（\ xi）\ H ^ n（B; \ k）$中的Euler类消失时，或等效地，当Thom空间的方向类具有平凡平方时，它具有特别简单的形式。由于我们进行了同源性计算，我们能够显示出悬架谱$ \ Sigma ^ \ infty \ Omega M \ xi $具有局部分裂，从而在$ M \ xi $时取代了$ \ Sigma \ Omega M \ xi $的James分裂。是悬架。
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