A simple proof of the fundamental theorem of Kirby calculus on links

Lu, Ning

doi:10.1090/S0002-9947-1992-1065603-2

A simple proof of the fundamental theorem of Kirby calculus on links
HTML articles powered by AMS MathViewer

by Ning Lu PDF

Trans. Amer. Math. Soc. 331 (1992), 143-156 Request permission

Abstract:

In this paper, we relate surgeries on links and Heegaard decompositions, relate framed links and surface mapping classes, and give a simple proof of the fundamental theorem of Kirby calculus on links by the presentation of the surface mapping class groups.

References

Joan S. Birman, Mapping class groups of surfaces, Braids (Santa Cruz, CA, 1986) Contemp. Math., vol. 78, Amer. Math. Soc., Providence, RI, 1988, pp. 13–43. MR 975076, DOI 10.1090/conm/078/975076
Roger Fenn and Colin Rourke, On Kirby’s calculus of links, Topology 18 (1979), no. 1, 1–15. MR 528232, DOI 10.1016/0040-9383(79)90010-7
Robion Kirby, A calculus for framed links in $S^{3}$, Invent. Math. 45 (1978), no. 1, 35–56. MR 467753, DOI 10.1007/BF01406222
W. B. R. Lickorish, A representation of orientable combinatorial $3$-manifolds, Ann. of Math. (2) 76 (1962), 531–540. MR 151948, DOI 10.2307/1970373
Ning Lu, Homeomorphisms of a solid handlebody and Heegaard splittings of the $3$-sphere $\textbf {S}^3$, Topology Proc. 13 (1988), no. 2, 325–350. MR 1053702
Dale Rolfsen, Rational surgery calculus: extension of Kirby’s theorem, Pacific J. Math. 110 (1984), no. 2, 377–386. MR 726496
Bronislaw Wajnryb, A simple presentation for the mapping class group of an orientable surface, Israel J. Math. 45 (1983), no. 2-3, 157–174. MR 719117, DOI 10.1007/BF02774014
Andrew H. Wallace, Modifications and cobounding manifolds, Canadian J. Math. 12 (1960), 503–528. MR 125588, DOI 10.4153/CJM-1960-045-7