The purpose of the present paper is twofold: first to extend to non-orientable compact 4-manifolds the notion of gem-induced trisection, directly obtained from colored triangulations (or, equivalently, from colored graphs encoding them, called gems); second to prove that, both in the orientable and non-orientable case, if the boundary is homeomorphic to a connected sum of sphere bundles over S^1, gem-induced trisections naturally give rise to trisections of the corresponding closed 4-manifold. As a consequence, an estimation of the trisection genus of any closed orientable 4-manifold is obtained via colored triangulations, in terms of the combinatorial properties of a Kirby diagram representing it.
Trisections of PL 4-Manifolds Arising from Colored Triangulations / Casali, M. R.; Cristofori, P.. - In: MEDITERRANEAN JOURNAL OF MATHEMATICS. - ISSN 1660-5454. - 22:1(2025), pp. N/A-N/A. [10.1007/s00009-024-02790-2]
Trisections of PL 4-Manifolds Arising from Colored Triangulations
M. R. Casali;P. Cristofori
2025
Abstract
The purpose of the present paper is twofold: first to extend to non-orientable compact 4-manifolds the notion of gem-induced trisection, directly obtained from colored triangulations (or, equivalently, from colored graphs encoding them, called gems); second to prove that, both in the orientable and non-orientable case, if the boundary is homeomorphic to a connected sum of sphere bundles over S^1, gem-induced trisections naturally give rise to trisections of the corresponding closed 4-manifold. As a consequence, an estimation of the trisection genus of any closed orientable 4-manifold is obtained via colored triangulations, in terms of the combinatorial properties of a Kirby diagram representing it.File | Dimensione | Formato | |
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