- Tytuł:
- Surfaces in 3-space that do not lift to embeddings in 4-space
- Autorzy:
-
Carter, J.
Saito, Masahico - Powiązania:
- https://bibliotekanauki.pl/articles/1342343.pdf
- Data publikacji:
- 1998
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
orientations
triple points
Boy's surface
knotted surfaces - Opis:
- A necessary and sufficient condition for an immersed surface in 3-space to be lifted to an embedding in 4-space is given in terms of colorings of the preimage of the double point set. Giller's example and two new examples of non-liftable generic surfaces in 3-space are presented. One of these examples has branch points. The other is based on a construction similar to the construction of Giller's example in which the orientation double cover of a surface with odd Euler characteristic is immersed in general position. A similar example is shown to be liftable with an explicit lifting given. The problem of lifting is discussed in relation to the theory of surface braids. Finally, the orientations of the double point sets are studied in relation to the lifting problem.
- Źródło:
-
Banach Center Publications; 1998, 42, 1; 29-47
0137-6934 - Pojawia się w:
- Banach Center Publications
- Dostawca treści:
- Biblioteka Nauki
Artykuł