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Rojo, JAuthor

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June 28, 2021
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A K-CONTACT SIMPLY CONNECTED 5-MANIFOLD WITH NO SEMI-REGULAR SASAKIAN STRUCTURE

Publicated to: PUBLICACIONS MATEMATIQUES. 65 (2): 615-651 - 2021-01-01 65(2), DOI: 10.5565/PUBLMAT6522107

Authors:

Cañas, A; Muñoz, V; Rojo, J; Viruel, A
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Affiliations

Univ Malaga, Dept Algebra Geometria & Topol, Campus Teatinos,S-N, E-29071 Malaga, Spain - Author
Univ Politecn Madrid, ETSI Ingn Informat, Campus Montegancedo, E-28660 Madrid, Spain - Author

Abstract

We construct the first example of a 5-dimensional simply connected compact manifold that admits a K-contact structure but does not admit any semi-regular Sasakian structure. For this, we need two ingredients: (a) to construct a suitable simply connected symplectic 4-manifold with disjoint symplectic surfaces spanning the homology, all of them of genus 1 except for one of genus g > 1; (b) to prove a bound on the second Betti number b(2) of an algebraic surface with b(1) = 0 and having disjoint complex curves spanning the homology, all of them of genus 1 except for one of genus g > 1.
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Keywords

Algebraic surfaceK-contactSasakianSeifert bundleSmale-barden manifoldSmale–barden manifold

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal PUBLICACIONS MATEMATIQUES due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2021, it was in position 72/333, thus managing to position itself as a Q1 (Primer Cuartil), in the category Mathematics.

Independientemente del impacto esperado determinado por el canal de difusión, es importante destacar el impacto real observado de la propia aportación.

Según las diferentes agencias de indexación, el número de citas acumuladas por esta publicación hasta la fecha 2026-04-27:

  • WoS: 3
  • Scopus: 4
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Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2026-04-27:

  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 1 (PlumX).

It is essential to present evidence supporting full alignment with institutional principles and guidelines on Open Science and the Conservation and Dissemination of Intellectual Heritage. A clear example of this is:

  • The work has been submitted to a journal whose editorial policy allows open Open Access publication.
  • Assignment of a Handle/URN as an identifier within the deposit in the Institutional Repository: https://oa.upm.es/93204/

As a result of the publication of the work in the institutional repository, statistical usage data has been obtained that reflects its impact. In terms of dissemination, we can state that, as of

  • Views: 26
  • Downloads: 6
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Leadership analysis of institutional authors

There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: Last Author (Viruel, A).

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Project objectives

La aportación persigue los siguientes objetivos principales: construir un ejemplo de variedad compacta simplemente conexa de dimensión cinco que admita una estructura K-contacto; demostrar que dicha variedad no admite ninguna estructura Sasakiana semi-regular; diseñar una variedad simpléctica simplemente conexa de dimensión cuatro con superficies simplécticas disjuntas que generen la homología, donde todas tienen género 1 salvo una de género g > 1; y establecer un límite para el segundo número de Betti b(2) de una superficie algebraica con b(1) = 0 que contenga curvas complejas disjuntas generadoras de la homología, con géneros similares a los descritos. Estos objetivos permiten avanzar en la comprensión de las estructuras geométricas en variedades de alta dimensión.
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Most relevant results

El estudio presenta avances significativos en la geometría diferencial de variedades compactas. En primer lugar, se construye el primer ejemplo de una variedad compacta simplemente conexa de dimensión cinco que admite una estructura K-contacta pero carece de cualquier estructura Sasakiana semi-regular. En segundo lugar, se desarrolla una variedad simpléctica simplemente conexa de dimensión cuatro con superficies simplécticas disjuntas que generan la homología, donde todas tienen género 1 salvo una de género g > 1. Finalmente, se establece una cota para el segundo número de Betti b(2) de una superficie algebraica con b(1) = 0 que posee curvas complejas disjuntas generadoras de la homología, con géneros análogos a los mencionados.
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Awards linked to the item

We are grateful to Enrique Arrondo, Alex Tralle, Fran Presas, and Roger Casals for useful comments. We are also grateful to the two anonymous referees that have given us numerous comments. The second author is partially supported by Project MINECO (Spain) PGC2018-095448-B-I00. The fourth author is partially supported by Project MINECO (Spain) MTM2016-78647-P.
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