Bridge trisections and classical knotted surface theory
| Autor: | Jason Joseph, Jeffrey Meier, Maggie Miller, Alexander Zupan |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Pacific Journal of Mathematics |
| ISSN: | 1945-5844 0030-8730 |
| Popis: | We seek to connect ideas in the theory of bridge trisections with other well-studied facets of classical knotted surface theory. First, we show how the normal Euler number can be computed from a tri-plane diagram, and we use this to give a trisection-theoretic proof of the Whitney-Massey Theorem, which bounds the possible values of this number in terms of the Euler characteristic. Second, we describe in detail how to compute the fundamental group and related invariants from a tri-plane diagram, and we use this, together with an analysis of bridge trisections of ribbon surfaces, to produce an infinite family of knotted spheres that admit non-isotopic bridge trisections of minimal complexity. v1 has been divided into two papers: the present article and "Bridge trisections and Seifert solids," which will be posted simultaneously; 29 pages, 11 figures |
| Databáze: | OpenAIRE |
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