Note on a conjecture of Stephen Halperin’s. (English) Zbl 0708.55008
Topology and combinatorial group theory, Proc. Fall Foliage Topology Semin., New Hampshire/UK 1986-88, Lect. Notes Math. 1440, 148-163 (1990).
[For the entire collection see Zbl 0701.00019.]
The S. Halperin conjecture can be stated as follows: For any orientable fibration \(F\to E\to B\), where F is a 1-connected space with both finite rational homology and homotopy and positive Euler characteristic then the Serre spectral sequence - with rational coefficients - of the fibration collapses at the \(E_ 2\)-term. This conjecture has been proved for a number of special cases. This note proves the conjecture in the case that \(H^*(F;{\mathbb{Q}})\) has three generators.
The S. Halperin conjecture can be stated as follows: For any orientable fibration \(F\to E\to B\), where F is a 1-connected space with both finite rational homology and homotopy and positive Euler characteristic then the Serre spectral sequence - with rational coefficients - of the fibration collapses at the \(E_ 2\)-term. This conjecture has been proved for a number of special cases. This note proves the conjecture in the case that \(H^*(F;{\mathbb{Q}})\) has three generators.
Reviewer: J.C.Thomas
MSC:
| 55P62 | Rational homotopy theory |
