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Non-formal co-symplectic manifolds


Authors: Giovanni Bazzoni, Marisa Fernández and Vicente Muñoz
Journal: Trans. Amer. Math. Soc. 367 (2015), 4459-4481
MSC (2010): Primary 53C15, 55S30; Secondary 53D35, 55P62, 57R17
DOI: https://doi.org/10.1090/S0002-9947-2014-06361-7
Published electronically: September 4, 2014
MathSciNet review: 3324935
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Abstract: We study the formality of the mapping torus of an orientation-preserving diffeomorphism of a manifold. In particular, we give conditions under which a mapping torus has a non-zero Massey product. As an application we prove that there are non-formal compact co-symplectic manifolds of dimension $ m$ and with first Betti number $ b$ if and only if $ m=3$ and $ b \geq 2$, or $ m \geq 5$ and $ b \geq 1$. Explicit examples for each one of these cases are given.


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Giovanni Bazzoni
Affiliation: Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, Consejo Superior de Investigaciones Científicas, C/ Nicolas Cabrera 13-15, 28049 Madrid, Spain
Email: gbazzoni@icmat.es

Marisa Fernández
Affiliation: Facultad de Ciencia y Tecnología, Departamento de Matemáticas, Universidad del País Vasco, Apartado 644, 48080 Bilbao, Spain
Email: marisa.fernandez@ehu.es

Vicente Muñoz
Affiliation: Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid, Spain
Email: vicente.munoz@mat.ucm.es

DOI: https://doi.org/10.1090/S0002-9947-2014-06361-7
Keywords: Co-symplectic manifold, mapping torus, minimal model, formal manifold.
Received by editor(s): January 10, 2013
Received by editor(s) in revised form: December 23, 2013
Published electronically: September 4, 2014
Additional Notes: The first and third authors were partially supported by Project MICINN (Spain) MTM2010-17389. The second author was partially supported through Project MICINN (Spain) MTM2011-28326-C02-02, and Project of UPV/EHU ref. UFI11/52
Article copyright: © Copyright 2014 American Mathematical Society