Multisections of surface bundles and bundles over S1

• Autores: Delphine Moussard
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 69, Nº 1, 2025, págs. 147-161
• Idioma: inglés
• DOI: 10.5565/publmat6912506
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• Resumen

  • A multisection is a decomposition of a manifold into 1-handlebodies, where each subcollection of the pieces intersects along a 1-handlebody except the global intersection, which is a closed surface. These generalizations of Heegaard splittings and Gay-Kirby trisections were introduced by Ben Aribi, Courte, Golla, and the author, who proved in particular that any 5-manifold admits such a multisection. In arbitrary dimension, we show that two classes of manifolds admit multisections: surface bundles and fiber bundles over the circle, whose fiber itself is multisected. We provide explicit constructions, with examples.

• Referencias bibliográficas
  • F. Ben Aribi, S. Courte, M. Golla, and D. Moussard, Multisections of higher-dimensional manifolds, Preprint (2023). arXiv:2303.08779.
  • D. T. Gay and R. Kirby, Trisecting 4-manifolds, Geom. Topol. 20(6) (2016), 3097–3132. DOI: 10.2140/gt.2016.20.3097
  • G. Islambouli and P. Naylor, Multisections of 4-manifolds, Trans. Amer. Math. Soc. 377(2) (2024), 1033–1068. DOI: 10.1090/tran/8996
  • K. Johannson, Topology and Combinatorics of 3-Manifolds, Lecture Notes in Math. 1599, Springer-Verlag, Berlin, 1995. DOI: 10.1007/BFb0074005
  • D. Koenig, Trisections of 3-manifold bundles over S1, Algebr. Geom. Topol. 21(6) (2021), 2677–2702. DOI: 10.2140/agt.2021.21.2677
  • C. P. Rourke and B. J. Sanderson, Introduction to Piecewise-Linear Topology, Reprint, Springer Study Ed., Springer-Verlag, Berlin-New York,...
  • J. H. Rubinstein and S. Tillmann, Multisections of piecewise linear manifolds, Indiana Univ. Math. J. 69(6) (2020), 2209–2239. DOI: 10.1512/iumj.2020.69.8044
  • M. Williams, Trisections of flat surface bundles over surfaces, Thesis (Ph.D.)-The University of Nebraska - Lincoln (2020).