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