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

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Suppose that   is a fibration of simply connected spaces such that   is rationally elliptic and   (i.e.,   has non-zero Euler characteristic), then the Serre spectral sequence associated to the fibration collapses at the   page.[1]

Status

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As of 2019, Halperin's conjecture is still open. Gregory Lupton has reformulated the conjecture in terms of formality relations.[2]

Notes

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  1. ^ Berglund, Alexander (2012), Rational homotopy theory (PDF)
  2. ^ Lupton, Gregory (1997), "Variations on a conjecture of Halperin", Homotopy and Geometry (Warsaw, 1997), arXiv:math/0010124, MR 1679854

Further reading

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