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Crosscap Numbers of Two -component Links

Gengyu Zhang
경북대학교 자연과학대학 수학과|2008.06|Kyungpook Mathematical Journal|제48권 제2호|pp. 241-254

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참고문헌

키워드

crosscap numbertwo-component linklinking formGoeritz matrixnon-orientable surface
주제분류수학

초록

We define the crosscap number of a 2-component link as the minimum of the first Betti numbers of connected, non-orientable surfaces bounding the link. We discuss some properties of the crosscap numbers of 2-component links.

Abstract

We define the crosscap number of a 2-component link as the minimum of the first Betti numbers of connected, non-orientable surfaces bounding the link. We discuss some properties of the crosscap numbers of 2-component links.

참고문헌 (11)

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  2. C. McA. Gordon, "On the signature of a link (MR 0500905 (58 #18407))", Invent. Math, 47(1), pp.53~69 (1978)
  3. M. Hirasawa, "Crosscap numbers of 2-bridge knots", Topology, 45(3), pp.513~530 (2006)
  4. 0608480), "Crosscap numbers of pretzel knots (GT", K. Ichihara
  5. W. B. R. Lickorish, "An Introduction to Knot Theory, Graduate Texts in Mathematics (MR 1472978 (98f:57015))", Springer-Verlag New York, 175 (1997)
  6. H. Murakami, "Crosscap number of a knot MR 1362987 (96k:57006))", Pacific J. Math, 171(1), pp.261~273 (1995)
  7. K. Murasu, "On the signature of links (MR 0261585 (41 #6198))", Topology, 9, pp.283~298 (1970)
  8. I. Niven, "An Introduction to the Theory of Numbers (MR 1083765 (91i:11001))" (1991), John Wiley & Sons Inc., New York
  9. D. Rolfsen, "Knots and Links, Mathematics Lecture Series (MR 95c:57018)", Publish or Perish Inc. Houston TX, 7 (1990)
  10. M. Teragaito, "Crosscap numbers of torus knots (MR 2035482 (2005a:57007))", Topology Appl, 138(1), pp.219~238 (2004)
  11. H. F. Trotter, "Homology of group systems with applications to knot theory (MR 0143201 (26 #761))", Ann. of Math, 76(2), pp.464~498 (1962)

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