The rational Toomer invariant and certain elliptic spaces. (English) Zbl 1041.55008
Cornea, O. (ed.) et al., Lusternik-Schnirelmann category and related topics. Proceedings of the 2001 AMS-IMS-SIAM joint summer research conference on Lusternik-Schnirelmann category in the new millennium, South Hadley, MA, USA, July 29–August 2, 2001. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-2800-2/pbk). Contemp. Math. 316, 135-146 (2002).
In this well written paper, the author gives an explicit formula for the Toomer invariant of an elliptic rational space admitting a minimal model with homogeneous differential. He also proves that for such spaces, the set of Toomer invariants of the individual cohomology classes contains no gaps, partially answering a question of Y. Félix. Under the additional hypothesis that the rational Hurewicz homomorphism is non-zero in some odd degree, he deduces a lower bound for the total dimension of the cohomology, namely twice the Toomer invariant of the space.
For the entire collection see [Zbl 1005.00038].
For the entire collection see [Zbl 1005.00038].
Reviewer: Clemens Berger (Nice)
MSC:
| 55P62 | Rational homotopy theory |
| 55M30 | Lyusternik-Shnirel’man category of a space, topological complexity à la Farber, topological robotics (topological aspects) |
| 55T10 | Serre spectral sequences |
