- A note on the involutive concordance invariants of certain (1,1)-knots
- Project Year:
2021
- REU Student (s):
Anna Antal | Rutgers University-New Brunswick NJ
| Sarah Pritchard | Georgia Institute of Technology-Main Campus GA
- Student 1 Institution:
Rutgers University-New Brunswick
- Student 2 Institution:
Georgia Institute of Technology-Main Campus
- Project Mentor:
Kristen Hendricks
- Project Mentor Area:
Mathematics
- Project Abstract:
In this project we worked with involutive Heegaard Floer homology, developed by Hendricks and Manolescu as a refinement to Heegaard Floer homology. Involutive Heegaard Floer homology introduced two new knot concordance invariants. These invariants are interesting, because unlike other concordance invariants like τ, ε, and ν, they do not necessarily vanish on knots of finite concordance order, like the figure-eight knot. We computed these two new invariants for all non-thin and non-L-space 10 and 11-crossing (1,1)-knots for which they were not yet known. We also studied (1,1)-diagrams, and the relationships between them and the resulting CFK^∞ chain complexes.
