Studies on partial orders on sets of 3-manifolds defined by epimorphisms between fundamental groups.

对于最多有11个交叉点的素数纽结集合，我们确定了利用纽结群之间的保经满同态定义的偏序关系。我们还证明了对于任一给定的2-桥结，存在一个由零度映射诱导的具有满态射的Montesinos纽结。此外，我们还发现了不是由非零度映射诱导的3桥双曲Montsinos纽结和2桥双曲纽结对。对于有限素数域上的二维特殊线性群，存在无穷多个素数使得其纽结群上存在一个非阿贝尔表示.

For the set of prime knots with up to 11-crossings, we determined the partial order relation defined by using meridian preserving epimorphisms between knots groups. We also proved that for any given 2-bridge knot there exists a Montesinos knot with an epimorphims which is induced by a degree zero map. Further we found pairs of a 3-bridge hyperbolic Montsinos knot and a 2-bridge hyperbolic knot which is not induced from a nonzero degree map. For any knot, there exists a infinitely many prime numbers such that there exists a non abelian representation on its knot group in 2-dimensional special linear group over a finite prime field with such a characteristic.