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On infinite classes of genus two 1-bridge knots

김수환|Yangkok Kim
대한수학회 (The Korean Mathematical Society)|2004.07|대한수학회논문집 (Communications of the KMS)|제19권 제3호|pp. 531-544

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Abstract

We study a family of 2-bridge knots with 2-tangles in the 3-sphere admitting a genus two 1-bridge splitting. We also observe a geometric relation between (g ¡ 1; 1)-splitting and (g; 0)- splitting for g = 2; 3. Moreover we construct a family of closed orientable 3-manifolds which are n-fold cyclic coverings of the 3- sphere branched over those 2-bridge knots.

참고문헌 (9)

  1. "The knots in D2 S1 with non-trivial Dehn surgery yieldingD2 D1", 38, pp.1~19 (1991)
  2. "Surgery on knots in solid tori", 28, pp.1~6 (1989)
  3. "1-bridge braids in solid tori", 37, pp.221~235 (1990)
  4. "Genus two Heegaard splittings of exteriorsof knots and the disjoint curve property"
  5. "Classication of unknotting tunnels for two bridge knots", 2, pp.259~290 (1999)
  6. "Heegaard splittings of exteriors of two bridge knots", 5, pp.609~651 (2001)
  7. "Incompressibility of surfaces in surgered 3-manifold", 32, pp.271~279 (1992)
  8. "@-reducing Dehn surgeries and 1-bridge knots", 295, pp.319~331 (1992)
  9. "Incompressible surfaces and Dehn surgery on 1-bridge knots in handle-bodies", 120, pp.687~696 (1996)

관련 논문AI추천

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