Multiplicative Aspects of the Halperin-Carlsson Conjecture

Details Multiplicative Aspects of the Halperin-Carlsson Conjecture Multiplicative Aspects of the Halperin-Carlsson Conjecture

2008-11-21

arxiv.org/abs/0811.3517v1

Mathematics

Algebraic Topology

Scientific paper

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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