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Some open book and contact structures on moment-angle manifolds

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Abstract

I. We construct open book structures on all moment-angle manifolds and describe the topology of their leaves and bindings under certain restrictions. II. We also show, using a recent deep result about contact forms due to Borman et al. (Acta Math 215:281–361, 2015), that every odd-dimensional moment-angle manifold admits a contact structure. This contrasts with the fact that, except for a few, well-determined cases, even-dimensional ones do not admit symplectic structures. We obtain the same results for large families of more general intersections of quadrics.

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Notes

  1. The retraction \(Z\rightarrow Z_{_+}\) induces an epimorphism in homology and fundamental group.

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Authors and Affiliations

  1. Universidad Aeronáutica en Querétaro, Carretera Estatal Querétaro-Tequisquiapan 22154, 76270, Colón, Qro, Mexico

    Yadira Barreto

  2. Instituto de Matemáticas, Universidad Nacional Autónoma de México, Coyoacán, 04510, Mexico, DF, Mexico

    Santiago López de Medrano

  3. Instituto de Matemáticas, Unidad Cuernavaca, Universidad Nacional Autónoma de México, Av. Universidad s/n, Col. Lomas de Chamilpa, 62209, Cuernavaca, Morelos, Mexico

    Alberto Verjovsky

Authors
  1. Yadira Barreto
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  2. Santiago López de Medrano
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  3. Alberto Verjovsky
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Corresponding author

Correspondence to Santiago López de Medrano.

Additional information

In memory of Samuel Gitler.

The authors were partially supported by projects PAPIIT-DGAPA IN103914 and IN108112.

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Barreto, Y., López de Medrano, S. & Verjovsky, A. Some open book and contact structures on moment-angle manifolds. Bol. Soc. Mat. Mex. 23, 423–437 (2017). https://doi.org/10.1007/s40590-016-0113-y

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  • DOI: https://doi.org/10.1007/s40590-016-0113-y

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