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math.GT2026
Non-kinetic homotopy coherent actions on four-manifolds
Sungkyung Kang, JungHwan Park, Masaki Taniguchi
We give the first example of a non-kinetic smooth homotopy coherent action of order two on a closed simply connected smooth four-manifold. This action is obtained by restricting a…
math.GT2026
Unknotting number, ribbon concordance, and singular instantons
Hayato Imori, JungHwan Park, Masaki Taniguchi
We use equivariant singular instanton Floer theory with the Chern--Simons filtration to obstruct same-sign unknotting operations. We show that, for a large class of slice knots obt…
math.GT2026
Forbidden configurations and definite fillings of lens spaces
Antony T. H. Fung, JungHwan Park
We study definite fillings of lens spaces. We classify the lens spaces for which every smooth negative-definite filling satisfies \[ b_2(X)\ge b_2(X(p,q))-1, \] where…