Halperin-Carlsson猜想的乘法性质
Multiplicative Aspects of the Halperin-Carlsson Conjecture
摘要：
我们利用Koszul分解的乘法结构给出了一些已知的上同调总维度估计的简短证明，这些估计允许自由环面作用，并给出了多项式环上过滤微分模的类似结果。我们还指出，在所谓的最小Hirsch-Brown模型的空间的等变上同调的乘法结构的存在下，改善这些结果的可能性。
英文摘要：
We use the multiplicative structure of the Koszul resolution to give short and simple proofs of some known estimates for the total dimension of the cohomology of spaces which admit free torus actions and analogous results for filtered differential modules over polynomial rings. We also point out the possibility of improving these results in the presence of a multiplicative structure on the so-called minimal Hirsch-Brown model for the equivariant cohomology of the space.
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