#### 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.