Year: 2025
Type: article
Abstract: We continue our study of the integer-valued knot invariants ν ♯ ( K ) \nu ^\sharp (K) and r 0 ( K ) r_0(K) , which together determine the dimensions of the framed instanton homologies of all nonzero Dehn surgeries on K 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 ♯ ( K ) \nu ^\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 ♯ ( K ) \epsilon ^\sharp (K) of Hom’s ϵ \epsilon -invariant in Heegaard Floer homology, and to the problem of characterizing a given 3-manifold as Dehn surgery on a knot in S 3 S^3 .
DOI: 10.1090/tran/9320
Authors: John Baldwin, Steven Sivek
Institutions: Boston College, Imperial College London
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4417046602