#### Presentation Title

P-37 Self and Mixed Delta Moves on Algebraically Split Links

#### Presenter Status

Undergraduate, Mathematics

#### Second Presenter Status

Undergraduate, Mathematics

#### Third Presenter Status

Undergraduate, Engineering

#### Fourth Presenter Status

Undergraduate, Physics

#### Fifth Presenter Status

Professor, 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

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 showing links related by a self Delta-move for algebraically split links with up to 9-crossings. For these links we also determine the Delta-splitting number and mixed Delta-splitting number, that is, the minimum number of Delta-moves needed to separate the components of the link.

P-37 Self and Mixed Delta Moves on Algebraically Split Links

Buller Hall Hallways

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 showing links related by a self Delta-move for algebraically split links with up to 9-crossings. For these links we also determine the Delta-splitting number and mixed Delta-splitting number, that is, the minimum number of Delta-moves needed to separate the components of the link.

## Acknowledgments

Adviser: Prof. Anthony Bosman, Department of Mathematics and support from the Mathematical Association of America and National Science Foundation