Halperin conjecture

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 is a fibration of simply [connected space]s such that is Rational homotopy theory#Elliptic and [hyperbolic spaces|rationally elliptic] and , then the Serre spectral sequence associated to the fibration collapses at the page.

Status

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