Embedding compact surfaces into the 3-dimensional Euclidean space with maximum symmetry
The symmetries of surfaces which can be embedded into the symmetries of the 3-dimensional Euclidean space R3 are easier to feel by human's intuition. We give the maximum order of finite group actions on (R3 E) among all possible embedded closed/bordered surfaces with given geometric/algebraic genus...
Gespeichert in:
Veröffentlicht in: | Science China. Mathematics 2017-09, Vol.60 (9), p.1599-1614 |
---|---|
Hauptverfasser: | , , , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Zusammenfassung: | The symmetries of surfaces which can be embedded into the symmetries of the 3-dimensional Euclidean space R3 are easier to feel by human's intuition. We give the maximum order of finite group actions on (R3 E) among all possible embedded closed/bordered surfaces with given geometric/algebraic genus greater than 1 in R3. We also identify the topological types of the bordered surfaces realizing the maximum order, and findsimple representative embeddings for such surfaces. |
---|---|
ISSN: | 1674-7283 1869-1862 |
DOI: | 10.1007/s11425-017-9078-0 |