Nontrivial embeddings of polygonal intervals and unknots in 3-space

Authors
Cantarella, J Johnston, H
Citation
J. Cantarella et H. Johnston, Nontrivial embeddings of polygonal intervals and unknots in 3-space, J KNOT TH R, 7(8), 1998, pp. 1027-1039
Citations number
6
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS
ISSN journal
02182165 → ACNP
Volume
7
Issue
8
Year of publication
1998
Pages
1027 - 1039
Database
ISI
SICI code
0218-2165(199812)7:8<1027:NEOPIA>2.0.ZU;2-T
Abstract
We consider embedding classes of polygonal intervals and circles with fixed edge lengths. We classify all embeddings of polygonal lines of five segmen ts, finding that this space has three connected components for suitable edg e lengths. We then construct a class of "stuck" unknotted hexagons, which c annot be deformed to the standard unknotted hexagon. The edge lengths of ou r examples are not equal.