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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Non-formal co-symplectic manifolds
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by Giovanni Bazzoni, Marisa Fernández and Vicente Muñoz PDF
Trans. Amer. Math. Soc. 367 (2015), 4459-4481 Request permission


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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Additional Information
  • 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:
  • Marisa Fernández
  • Affiliation: Facultad de Ciencia y Tecnología, Departamento de Matemáticas, Universidad del País Vasco, Apartado 644, 48080 Bilbao, Spain
  • Email:
  • Vicente Muñoz
  • Affiliation: Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid, Spain
  • Email:
  • 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
  • © Copyright 2014 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 367 (2015), 4459-4481
  • MSC (2010): Primary 53C15, 55S30; Secondary 53D35, 55P62, 57R17
  • DOI:
  • MathSciNet review: 3324935