Variations on a conjecture of Halperin

Gregory Lupton

Banach Center Publications (1998)

  • Volume: 45, Issue: 1, page 115-135
  • ISSN: 0137-6934

Abstract

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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 E 2 -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.

How to cite

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Lupton, Gregory. "Variations on a conjecture of Halperin." Banach Center Publications 45.1 (1998): 115-135. <http://eudml.org/doc/208897>.

@article{Lupton1998,
abstract = {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 $E_2$-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.},
author = {Lupton, Gregory},
journal = {Banach Center Publications},
keywords = {Halperin conjecture; ellipctic spaces; formal spaces; Lyusternik-Shnirel'man category},
language = {eng},
number = {1},
pages = {115-135},
title = {Variations on a conjecture of Halperin},
url = {http://eudml.org/doc/208897},
volume = {45},
year = {1998},
}

TY - JOUR
AU - Lupton, Gregory
TI - Variations on a conjecture of Halperin
JO - Banach Center Publications
PY - 1998
VL - 45
IS - 1
SP - 115
EP - 135
AB - 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 $E_2$-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.
LA - eng
KW - Halperin conjecture; ellipctic spaces; formal spaces; Lyusternik-Shnirel'man category
UR - http://eudml.org/doc/208897
ER -

References

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