Branched covers bounding rational homology balls

2020/02/29 by Paolo Aceto, Jeffrey Meier, Allison N. Miller +3
Mathematics · #Advanced Combinatorial Mathematics #Algebra over a field #Artificial intelligence #Biology #Bounding overwatch #Combinatorics #Computer science #Discrete mathematics #Geometric and Algebraic Topology #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Khovanov homology #Mathematics #Pure mathematics #math.GT

paper · pdf · doi:10.2140/agt.2021.21.3569

published as Algebr. Geom. Topol. 21 (2021) 3569-3599 · 19 pages, 5 figures, Version 2: Minor changes to abstract and introduction. Added references on knots that are not concordant to their reverses

arxiv created 2020/04/17 · openalex publication_date 2021/12/28 · arxiv updated 2022/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Prime power fold cyclic branched covers along smoothly slice knots all bound rational homology balls. This phenomenon, however, does not characterize slice knots. In this paper, we give a new construction of non-slice knots that have the above property. The sliceness obstruction comes from computing twisted Alexander polynomials, and we introduce new techniques to simplify their calculation.

Citations

• The topology of four-dimensional manifolds
• The knot Floer complex and the smooth concordance group
• Lens spaces, rational balls and the ribbon conjecture
• The structure of the rational concordance group of knots
• On rational sliceness of Miyazaki's fibered, −amphicheiral knots
• Concordance homomorphisms from knot Floer homology