On the degeneration ratio of tunnel numbers and free tangle decompositions of knots

@article{Morimoto2007OnTD,
  title={On the degeneration ratio of tunnel numbers and free tangle decompositions of knots},
  author={K. Morimoto},
  journal={arXiv: Geometric Topology},
  year={2007}
}
  • K. Morimoto
  • Published 2007
  • Mathematics
  • arXiv: Geometric Topology
In this paper, we introduce a notion called n/k-free tangle and study the degeneration ratio of tunnel numbers of knots. 

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Abstract In the present paper, we introduce three geometric invariants of knots K: t(K) , g 1 ( K ), h ( K ), and study the relationship among these invariants, connected sum and tangleExpand
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Abstract. We analyze how a family of essential annuli in a compact 3-manifold will induce, from a strongly irreducible generalized Heegaard splitting of the ambient manifold, generalized HeegaardExpand
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In this paper, we show that there are infinitely many tunnel number two knots K such that the tunnel number of K#K' is equal to two again for any 2-bridge knot K'. INTRODUCTION Let K be a knot in theExpand
Higashi-Nada Okamoto 8-9-1, Kobe 658-8501, Japan morimoto@konan-u.ac
  • jp Received: 5 December