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Full-Text Articles in Mathematics
P-36 The Delta-Crossing Number For Links, Zachary Duah
P-36 The Delta-Crossing Number For Links, Zachary Duah
Celebration of Research and Creative Scholarship
An m-component link is an embedding of m circles into 3-dimensional space; a 1-component link is called a knot. The diagram for a link may be drawn so that all crossings occur within delta tangles, collections of three crossings as appear in a delta move. The delta crossing number is defined to be the minimal number of delta tangles in such a diagram. The delta crossing number has been well-studied for knots but not for links with multiple components. Using bounds we determine the delta crossing number for several 2-component links with up to 8 crossings as well as for …
P-37 Self And Mixed Delta Moves On Algebraically Split Links, Justyce Goode, Davielle Smith, Yamil Kas-Danouche, Devin Garcia, Anthony Bosman
P-37 Self And Mixed Delta Moves On Algebraically Split Links, Justyce Goode, Davielle Smith, Yamil Kas-Danouche, Devin Garcia, Anthony Bosman
Celebration of Research and Creative Scholarship
A link is an embedding of circles into 3-dimensional space. A Delta-move is a local move on a link diagram. The Delta-Gordian distance between links measures the minimum number of Delta-moves needed to move between link diagrams. We place restrictions on the Delta-move by either requiring the move to only involve a single component of the link, called a self Delta-move, or multiple components of the link, called a mixed Delta-move. We prove a number of results on how (mixed/self) Delta-moves relate to classical link invariants including the Arf invariant and crossing number. This allows us to produce a graph …