Full paper in PDF:
$% R. Nikkuni, Sharp edge-homotopy on spatial graphs, Rev. Mat. Complut. 18
(2005), no. 1, 181–207.%$
Sharp Edge-Homotopy on Spatial Graphs
A sharp-move is known as an unknotting operation for knots. A self sharp-move is a sharp-move on a spatial graph where all strings in the move belong to the same spatial edge. We say that two spatial embeddings of a graph are sharp edge-homotopic if they are transformed into each other by self sharp-moves and ambient isotopies. We investigate how is the sharp edge-homotopy strong and classify all spatial theta curves completely up to sharp edge-homotopy. Moreover we mention a relationship between sharp edge-homotopy and delta edge (resp. vertex)-homotopy on spatial graphs.
Key words: spatial graph, sharp move, delta move.
2000 Mathematics Subject Classification: 57M25, 57M15, 05C10.