30 citations · 30 across the 3 of their papers we have counts for
3 papers
math.GT2025
Knot primality: knot Floer homology, metacyclic representations and twisted homology
Samantha Allen, Charles Livingston
We develop purely algebraic methods for proving that a knot is prime. Our approach uses the Heegaard Floer polynomial in conjunction with classical knot-theoretic methods: cyclic,…
math.GT2023
Using knot Floer invariants to detect prime knots
Samantha Allen, Charles Livingston, Misha Temkin +1
We present knot primality tests that are built from knot Floer homology. The most basic of these is a simply stated and elementary consequence of Heegaard Floer theory: if the two-…
math.GT1999★ 30 cited
Concordance and Mutation
P Kirk, C Livingston
We provide a framework for studying the interplay between concordance and positive mutation and identify some of the basic structures relating the two. The fundamental result in un…