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

Ryo NIKKUNI
Department of Mathematics
School of Education,
Waseda University,
Nishi-Waseda 1-6-1, Shinjuku-ku,
Tokyo, 169-8050, Japan

Received: April 29, 2004
Accepted: August 5, 2004
ABSTRACT

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.