Correction terms and the non-orientable slice genus

2016/07/27 by Golla, Marco, Marengon, Marco
#57M25 #57M27 #57R58 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1607.08117

Abstract

By considering negative surgeries on a knot K in S³, we derive a lower bound to the non-orientable slice genus γ₄(K) in terms of the signature σ(K) and the concordance invariants V_i(K), which strengthens a previous bound given by Batson, and which coincides with Ozsváth-Stipsicz-Szabó's bound in terms of their υ invariant for L-space knots and quasi-alternating knots. A curious feature of our bound is superadditivity, implying, for instance, that the bound on the stable non-orientable genus is sometimes better than the one on γ₄(K).

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