A note on PL-disks and rationally slice knots

2021/07/19 by Kristen Hendricks, Jennifer Hom, Hendricks, Kristen +5
Mathematics · Medicine · #57K18 #57Q60 #57R58 #Bone health and treatments #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2107.09022

openalex publication_date 2021/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We give infinitely many examples of manifold-knot pairs (Y, J) such that Y bounds an integer homology ball, J does not bound a non-locally-flat PL-disk in any integer homology ball, but J does bound a smoothly embedded disk in a rational homology ball. The proof relies on formal properties of involutive Heegaard Floer homology.

Citations

• Floer homology and knot complements
• Holomorphic disks and knot invariants

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• PL-genus of surfaces in homology balls
• A note on rationally slice knots
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• A 4-dimensional rational genus bound
• Heegaard Floer homology of Matsumoto's manifolds