2023/09/05 by Antonio Alfieri, Irving Dai, Alfieri, Antonio +5 · 1 citation
Mathematics · Medicine · #57R58 #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2309.02309
openalex publication_date 2023/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Building on the work of Nozaki, Sato and Taniguchi, we develop an instanton-theoretic invariant aimed at studying strong corks and equivariant bounding. Our construction utilizes the Chern-Simons filtration and is qualitatively different from previous Floer-theoretic methods used to address these questions. As an application, we give an example of a cork whose boundary involution does not extend over any 4-manifold X with H1(X, ℤ2) = 0 and b2(X) ≤ 1 , and a strong cork which survives stabilization by either of n\smash\mathbbCP2 or n\smash\mathbbCP2. We also prove that every nontrivial linear combination of 1/n-surgeries on the strongly invertible knot \smash946 constitutes a strong cork. Although Yang-Mills theory has been used to study corks via the Donaldson invariant, this is the first instance where the critical values of the Chern-Simons functional have been utilized to produce such examples. Finally, we discuss the geography question for nonorientable surfaces in the case of extremal normal Euler number.