Twisted homology cobordism invariants of knots in aspherical manifolds

2010/05/24 by Prudence Heck, Heck, Prudence
Mathematics · #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1005.4435

openalex publication_date 2010/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We fix a null-homologous, homotopically essential knot J in a 3-manifold with PTFA fundamental group and study concordance of knots that are homotopic to J. We construct an infinite family of knots that are characteristic to J, and then use L²-methods to show that they are not concordant to J.

Citations

• Knot concordance, Whitney towers and L 2 -signatures

Related

• Link concordance, homology cobordism, and Hirzebruch-type defects from iterated p-covers
• Almost-concordance of knots in aspherical 3-manifolds
• Homotopy properties of knots in prime manifolds
• Homology cobordism and classical knot invariants
• Rational knot concordance and homology cobordism