A Partial order on the set of prime knots with up to 11 crossings
A Partial order on the set of prime knots with up to 11 crossings
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具有最多 11 个交叉点的素结集的偏序
DOI：
10.1142/s0218216511008747
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
MINEKO MATSUMOTO and MASAAKI SUZUKI
中科院分区：
文献类型：
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作者：
KEIICHI HORIE;TERUAKI KITANO;MINEKO MATSUMOTO and MASAAKI SUZUKI
设K为S3中的一个素数结，G(K) = π1（S3- K）为结群。如果存在从G（K1）到G（K2）的满射同态，则记为K1≥K2。在本文中，我们在一组最多有11个交点的素数结点上确定了这种偏序。存在801个素数结点，然后应该考虑640,800个。满射同态的存在性可以通过显式构造得到证明。另一方面，满射同态的不存在性可以用亚历山大多项式和扭曲亚历山大多项式来证明。
Let K be a prime knot in S3and G(K) = π1(S3- K) the knot group. We write K1≥ K2if there exists a surjective homomorphism from G(K1) onto G(K2). In this paper, we determine this partial order on the set of prime knots with up to 11 crossings. There exist such 801 prime knots and then 640, 800 should be considered. The existence of a surjective homomorphism can be proved by constructing it explicitly. On the other hand, the non-existence of a surjective homomorphism can be proved by the Alexander polynomial and the twisted Alexander polynomial.