Classification of 3-manifolds by link correspondence and knot theory

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For our establishing canonical correspondences from the set of closed connected oriented 3-manifolds to the set of prime links and from the set of prime links to the delta set of integral lattice points, we completed the correspondence classifications for the integral lattice points of lengths up to 7. By joint works with Dr.I.Tayama, we completed the correspondence classification from the set of the prime links of lengths 8,9,10 to the delta set of integral lattice points. On Reni-Mecchia-Zimmermann's conjecture, the head investigator solved this conjecture affirmatively. Also, the head investigator estimated the triple point canceling number of a surface-knot and constructed an example of surface-knots with a sufficiently large difference between the triple point canceling number and the triple point number.