Artificial intelligent assistant

what is a delta move on a trefoil knot I saw some notes discuss delta move, but they just give part of the graph. What is it like if we do the delta move on a trefoil knot? Is it an unknot? ![enter image description here](

It depends _a lot_ on which position your trefoil is in when you perform the move. Just like a crossing change or any other surgery-related change depends on where you perform it.

However, if you are thinking of a trefoil in the classical position with three crossings, then _yes_ , the result is an unknot (you can unknot it by three Reidemeister I moves).

Using this you can now see how the result could be different: since the Delta move is local, you can perform it on a factor in a connected sum. If you perform it on the second factor in the sum $$3_1\sharp \ U$$ where $U$ is an unknot in a position as described above, you can obtain $$3_1\sharp\ 3_1$$ that is a sum of two trefoils, as the result of a Delta move on one trefoil.

xcX3v84RxoQ-4GxG32940ukFUIEgYdPy c332a48673ec83e30a274a3cb1b2fa18