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Halperin conjecture

From Wikipedia, the free encyclopedia

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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