Variations on a conjecture of Halperin
Lupton, Gregory
Banach Center Publications, Tome 43 (1998), p. 115-135 / Harvested from The Polish Digital Mathematics Library
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Halperin has conjectured that the Serre spectral sequence of any fibration that has fibre space a certain kind of elliptic space should collapse at the E2-term. In this paper we obtain an equivalent phrasing of this conjecture, in terms of formality relations between base and total spaces in such a fibration (Theorem 3.4). Also, we obtain results on relations between various numerical invariants of the base, total and fibre spaces in these fibrations. Some of our results give weak versions of Halperin’s conjecture (Remark 4.4 and Corollary 4.5). We go on to establish some of these weakened forms of the conjecture (Theorem 4.7). In the last section, we discuss extensions of our results and suggest some possibilities for future work.

Publié le : 1998-01-01
EUDML-ID : urn:eudml:doc:208897 
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Lupton, Gregory. Variations on a conjecture of Halperin. Banach Center Publications, Tome 43 (1998) pp. 115-135. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv45i1p115bwm/

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