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Mathematics > Geometric Topology

Title: Trisections of PL 4-manifolds arising from colored triangulations

Abstract: The purpose of the present paper is twofold: firstly 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); secondly to prove that, both in the orientable and non-orientable case, if the boundary is homeomorphic to a connected sum of sphere bundles over $\mathbb S^1$, 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 in terms of surgery description is obtained via colored triangulations.
Comments: 14 pages, 4 figures. The structure of the paper has been modified, with partial re-writing and re-ordering of some paragraphs and propositions, in order to clarify concepts and arguments. Moreover, some oversights have been corrected
Subjects: Geometric Topology (math.GT)
MSC classes: 57Q15 - 57K40 - 57M15
Cite as: arXiv:2312.01902 [math.GT]
  (or arXiv:2312.01902v2 [math.GT] for this version)

Submission history

From: Paola Cristofori [view email]
[v1] Mon, 4 Dec 2023 14:00:02 GMT (1837kb,D)
[v2] Mon, 22 Apr 2024 14:45:28 GMT (1837kb,D)

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