Presentation Title
Presenter Status
Student, Mathematics
Preferred Session
Poster Session
Location
Buller Hall Hallways
Start Date
21-10-2022 2:00 PM
End Date
21-10-2022 3:00 PM
Presentation Abstract
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 Tait's infinite family of 3-component links with unknotted components. Moreover, we prove that the difference between the delta crossing number and the delta unlinking number can be arbitrarily large.
P-36 The Delta-Crossing Number for Links
Buller Hall Hallways
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 Tait's infinite family of 3-component links with unknotted components. Moreover, we prove that the difference between the delta crossing number and the delta unlinking number can be arbitrarily large.
Acknowledgments
Special thanks to Professor Bosman and the Department of Mathematics.