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On homotopy K3 surfaces constructed by two knots and their applications

2015/01/20 by Masatsuna Tsuchiya, Tsuchiya, Masatsuna
Mathematics · Medicine · #57M25 (Secondary) #57R65 (Primary) #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M25 #msc:57R65

paper · pdf · doi:10.48550/arxiv.1501.04722

18 pages, 81 figures

arxiv created 2015/01/20 · openalex publication_date 2015/01/20 · arxiv updated 2015/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let LHT be a left handed trefoil knot and K be any knot. We define Mn(K) to be the homology 3-sphere which is represented by a simple link of LHT and LHT \sharp K with framings 0 and n respectively. Starting with this link, we construct homotopy K3 and spin rational homology K3 surfaces containing Mn(K). Then we apply the adjunction inequality to show that if n>2gns(K)-2, Mn(K) does not bound any smooth spin rational 4-ball, and that under the same assumption the negative n-twisted Whitehead double of LHT \sharp K is not a slice knot, where gns(K) is the n-shake genus of K.

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