Английская Википедия:Halperin conjecture
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In rational homotopy theory, the Halperin conjecture concerns the Serre spectral sequence of certain fibrations. It is named after the Canadian mathematician Stephen Halperin.
Statement
Suppose that <math> F \to E \to B </math> is a fibration of simply connected spaces such that <math> F </math> is rationally elliptic and <math> \chi(F) \neq 0 </math> (i.e., <math> F </math> has non-zero Euler characteristic), then the Serre spectral sequence associated to the fibration collapses at the <math> E_2 </math> page.[1]
Status
As of 2019, Halperin's conjecture is still open. Gregory Lupton has reformulated the conjecture in terms of formality relations.[2]
Notes
References
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