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Resumen

A trisection of a smooth 4-manifold is a decomposition into three simple pieces with nice intersection properties. Work by Gay and Kirby shows that every smooth, connected, orientable 4-manifold can be trisected. Natural problems in trisection theory are to exhibit trisections of certain classes of 4-manifolds and to determine the minimal trisection genus of a particular 4-manifold.

Let Σg denote the closed, connected, orientable surface of genus g. In this thesis, we show that the direct product Σg × Σh has a ((2g + 1)(2h + 1) + 1;2g + 2h)-trisection, and that these parameters are minimal. We provide a description of the trisection, and an algorithm to generate a corresponding trisection diagram given the values of g and h. We then extend this construction to arbitrary closed, flat surface bundles over surfaces with orientable fiber and orientable or non-orientable base. If the fundamental group of such a bundle has rank 2 - χ + 2h, where h is the genus of the fiber and χ is the Euler characteristic of the base, these trisections are again minimal

Detalles

Título
Trisections of Flat Surface Bundles over Surfaces
Autor
Williams, Marla
Año de publicación
2020
Editorial
ProQuest Dissertations & Theses
ISBN
9798664734669
Tipo de fuente
Tesis doctoral o tesina
Idioma de la publicación
English
ID del documento de ProQuest
2437426769
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.