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Geometry and topology
On PL embeddings of a 2-sphere in the 4-dimensional Euclidean space
D. V. Bolotov B. Verkin Institute for Low Temperature Physics and Engeneering, 47, Nauky ave., Kharkiv, 61103, Ukraine
Abstract:
We prove that there is no 2-convex $ PL $ embedding of $S^2$ in $ E^4$ in the form of a polyhedron, each vertex of which is incident to no more than 5 edges.
Keywords:
polyhedron, PL embedding, Euclidean space.
Received December 30, 2019, published August 3, 2021
Citation:
D. V. Bolotov, “On PL embeddings of a 2-sphere in the 4-dimensional Euclidean space”, Sib. Èlektron. Mat. Izv., 18:2 (2021), 867–883
Linking options:
https://www.mathnet.ru/eng/semr1407 https://www.mathnet.ru/eng/semr/v18/i2/p867
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