Detecting codimension one manifold factors with topographical techniques
| Autor: | Dušan Repovš, Denise M. Halverson |
|---|---|
| Jazyk: | angličtina |
| Předmět: |
Property (philosophy)
Dimension (graph theory) Disjoint sets Twisted crinkled ribbons property Fuzzy ribbons property law.invention Combinatorics Mathematics - Geometric Topology 57N75 57N15 law Mathematics::Category Theory Mathematics::Quantum Algebra 57P99 Astrophysics::Solar and Stellar Astrophysics Point (geometry) Generalized manifold Mathematics - General Topology Mathematics 53C70 General position property Resolvable Codimension Mathematics::Geometric Topology Topographical map pair Cell-like resolution Codimension one manifold factor Geometry and Topology Manifold (fluid mechanics) |
| Zdroj: | Topology and its Applications. (17):2870-2880 |
| ISSN: | 0166-8641 |
| DOI: | 10.1016/j.topol.2009.08.023 |
| Popis: | We prove recognition theorems for codimension one manifold factors of dimension $n \geq 4$. In particular, we formalize topographical methods and introduce three ribbons properties: the crinkled ribbons property, the twisted crinkled ribbons property, and the fuzzy ribbons property. We show that $X \times \mathbb{R}$ is a manifold in the cases when $X$ is a resolvable generalized manifold of finite dimension $n \geq 3$ with either: (1) the crinkled ribbons property; (2) the twisted crinkled ribbons property and the disjoint point disk property; or (3) the fuzzy ribbons property. |
| Databáze: | OpenAIRE |
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