A Fox-Milnor theorem for the Alexander polynomial of knotted 2-spheres\n in S⁴

2019/01/02 by Delphine Moussard, Moussard, Delphine, Emmanuel Wagner +1
Mathematics · #57M99 #57Q45 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1901.00474

openalex publication_date 2019/01/02 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

For knots in S³, it is well-known that the Alexander polynomial of a\nribbon knot factorizes as f(t)f(t^-1) for some polynomial f(t). By\ncontrast, the Alexander polynomial of a ribbon 2-knot is not even symmetric\nin general. Via an alternative notion of ribbon 2-knots, we give a\ntopological condition on a 2-knot that implies the factorization of the\nAlexander polynomial.\n

Related

• On Meta-monoids and the Fox-Milnor Condition
• Alexander polynomials of ribbon knots and virtual knots
• Twisted Alexander polynomials of 2-bridge knots
• Homotopy ribbon concordance and Alexander polynomials
• Log-concavity of the Alexander polynomial