2022/06/23 by John A. Baldwin, Baldwin, John A., Steven Sivek +1 · 4 citations
Mathematics · Medicine · #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2206.11531
openalex publication_date 2022/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We continue our study of the integer-valued knot invariants ν^\sharp(K) and r0(K), which together determine the dimensions of the framed instanton homologies of all nonzero Dehn surgeries on K. We first establish a "conjugation" symmetry for the decomposition of cobordism maps constructed in our earlier work, and use this to prove, among many other things, that ν^\sharp(K) is always either zero or odd. We then apply these technical results to study linear independence in the homology cobordism group, to define an instanton Floer analogue ε^\sharp(K) of Hom's ε-invariant in Heegaard Floer homology, and to the problem of characterizing a given 3-manifold as Dehn surgery on a knot in S3.