Geodesic
On Non-Integral Dehn Surgeries Creating Non-Orientable Surfaces
Canadian mathematical bulletin, Tome 49 (2006) no. 4, pp. 624-627

Voir la notice de l'article provenant de la source Cambridge University Press

For a non-trivial knot in the 3-sphere, only integral Dehn surgery can create a closed 3-manifold containing a projective plane. If we restrict ourselves to hyperbolic knots, the corresponding claim for a Klein bottle is still true. In contrast to these, we show that non-integral surgery on a hyperbolic knot can create a closed non-orientable surface of any genus greater than two.
DOI : 10.4153/CMB-2006-057-5
Mots-clés : 57M25, knot, Dehn surgery, non-orientable surface 
Teragaito, Masakazu. On Non-Integral Dehn Surgeries Creating Non-Orientable Surfaces. Canadian mathematical bulletin, Tome 49 (2006) no. 4, pp. 624-627. doi: 10.4153/CMB-2006-057-5
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[1] [1] Bredon, G. E. and Wood, J. W., Non-orientable surfaces in orientable 3-manifolds. Invent. Math. 7(1969), 83–110. Google Scholar

[2] [2] End, W., Non-orientable surfaces in 3-manifolds. Arch. Math. (Basel) 59(1992), no. 2, 173–185. Google Scholar

[3] [3] Gordon, C. McA. and Luecke, J., Only integral Dehn surgeries can yield reducible manifolds. Math. Proc. Cambridge Philos. Soc. 102(1987), no. 1, 97–101. Google Scholar

[4] [4] Gordon, C. McA. and Luecke, J., Dehn surgeries on knots creating essential tori. I. Comm. Anal. Geom. 3(1995), no. 3–4, 597–644. Google Scholar

[5] [5] Kawauchi, A., Classification of pretzel knots. Kobe J. Math. 2(1985), no. 1, 11–22. Google Scholar

[6] [6] Kronheimer, P., Mrowka, T., Ozsváth, P. and Szabó, Z.. Monopoles and lens space surgeries. Preprint. http://www.math.harvard.edu/_kronheim/lens.pdf Google Scholar

[7] [7] Matignon, D. and Sayari, N., Non-orientable surfaces and Dehn surgeries. Canad. J. Math. 56(2004), no. 5, 1022–1033. Google Scholar

[8] [8] Rolfsen, D., Knots and Links. Mathematics Lecture Series 7, Publish or Perish, Berkeley, CA, 1976. Google Scholar

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