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Rational approximations of sectional category and Poincaré duality


Authors: José Gabriel Carrasquel-Vera, Thomas Kahl and Lucile Vandembroucq
Journal: Proc. Amer. Math. Soc. 144 (2016), 909-915
MSC (2010): Primary 55M30, 55P62
DOI: https://doi.org/10.1090/proc12722
Published electronically: June 9, 2015
MathSciNet review: 3430865
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Abstract: Félix, Halperin, and Lemaire have shown that the rational module category $ \operatorname {Mcat}$ and the rational Toomer invariant $ e_0$ coincide for simply connected Poincaré duality complexes. We establish an analogue of this result for the sectional category of a fibration.


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José Gabriel Carrasquel-Vera
Affiliation: Institut de Recherche en Mathématique et Physique, Université catholique de Louvain, 2 Chemin du Cyclotron, 1348 Louvain-la-Neuve, Belgium
Email: jose.carrasquel@uclouvain.be

Thomas Kahl
Affiliation: Centro de Matemática, Universidade do Minho, Campus de Gualtar, 4710-057 Braga, Portugal
Email: kahl@math.uminho.pt

Lucile Vandembroucq
Affiliation: Centro de Matemática, Universidade do Minho, Campus de Gualtar, 4710-057 Braga, Portugal
Email: lucile@math.uminho.pt

DOI: https://doi.org/10.1090/proc12722
Keywords: Lusternik-Schnirelmann category, sectional category, topological complexity, Sullivan models, Poincar\'e duality
Received by editor(s): October 7, 2014
Received by editor(s) in revised form: January 8, 2015
Published electronically: June 9, 2015
Additional Notes: The research of the first author was supported by FEDER through the Ministerio de Educación y Ciencia project MTM2010-18089. The research of the second and third authors was supported by FCT - Fundação para a Ciência e a Tecnologia through projects PTDC/MAT/0938317/2008 and PEstOE/MAT/UI0013/2014.
Communicated by: Michael A. Mandell
Article copyright: © Copyright 2015 American Mathematical Society

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