Polynomial splittings of Casson-Gordon invariants

2001/02/15 by Se-Goo Kim, Kim, Se-Goo
Mathematics · Physics and Astronomy · #57M25 #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Nonlinear Waves and Solitons #math.GT #msc:57M25

paper · pdf · doi:10.48550/arxiv.math/0102112

20 pages, 3 figures; two correct partial forms of Gilmer's theorem included, notational and technical changes made, new Section 5 added

openalex publication_date 2001/02/15 · arxiv created 2003/09/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we prove that the Casson-Gordon invariants of the connected sum of two knots split when the Alexander polynomials of the knots are coprime. As one application, for any knot K, all but finitely many algebraically slice twisted doubles of K are linearly independent in the knot concordance group.

Related

• Polynomial splittings of metabelian von Neumann rho-invariants
• Primary decomposition of knot concordance and von Neumann rho-invariants
• Casson invariant of knots associated with divides
• Knots of Ten or Fewer Crossings of Algebraic Order Two
• Filtration of the classical knot concordance group and Casson-Gordon invariants