Year: 2025
Type: article
Abstract: A knitted surface is a surface with or without closed components smoothly properly embedded in [Formula: see text], which is a generalization of a braided surface. A knitted surface is called a 2-dimensional knit if its boundary is the closure of a trivial braid. From a 2-dimensional knit S, we obtain a surface-link in [Formula: see text] by taking the closure of S. We show that any surface-link is ambient isotopic to the closure of some 2-dimensional knit. Further, we consider another type of the closure of a knitted surface, called the plat closure. It is known that any trivial surface-knot is ambient isotopic to the plat closure of a knitted surface of degree 2. We show that the plat closure of any knitted surface of degree 2 is a trivial surface-link, and any trivial surface-link is ambient isotopic to the plat closure of a knitted surface of degree [Formula: see text]. We also show the same result for the closure of 2-dimensional knits of degree 2.
Authors: Inasa Nakamura, Jumpei Yasuda
Institutions: Saga University, The University of Osaka
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G2111910848
OpenAlex ID: W4415184608