Resumen de Sharp edge-homotopy on spatial graphs

Ryo Nikkuni

• 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 of liar by self sharp-moves and ambient isofopies. We investigate how is f he sharp edge-homotopy strong and classify all spatial that a curves completely up to sharp edge-homotopy. Moreover we mention a relationship between sharp edge-homotopy and delta edge (rasp. vertex)-homotopy on spatial graphs.