Irreducible $3$-manifolds of genus $3$ containing a $2$-sided projective plane
HTML articles powered by AMS MathViewer
- by Seiya Negami
- Proc. Amer. Math. Soc. 89 (1983), 545-550
- DOI: https://doi.org/10.1090/S0002-9939-1983-0715884-7
- PDF | Request permission
Abstract:
It will be shown that the minimum genus over all Heegaard splittings which yield irreducible closed $3$-manifolds containing a $2$-sided projective plane but not homeomorphic to ${P^2} \times {S^1}$ is equal to 3, with an infinite number of examples of genus 3.References
- Francis Bonahon, Difféotopies des espaces lenticulaires, Topology 22 (1983), no. 3, 305–314 (French). MR 710104, DOI 10.1016/0040-9383(83)90016-2
- Wolfgang Haken, Some results on surfaces in $3$-manifolds, Studies in Modern Topology, Math. Assoc. America, Buffalo, N.Y.; distributed by Prentice-Hall, Englewood Cliffs, N.J., 1968, pp. 39–98. MR 0224071 C. D. Hodgson, Involutions and isotopies of lens spaces, Master Thesis, Univ. of Melbourne, 1981.
- Tatsuo Homma and Mitsuyuki Ochiai, On relations of Heegaard diagrams and knots, Math. Sem. Notes Kobe Univ. 6 (1978), no. 2, 383–393. MR 512641
- William Jaco, Lectures on three-manifold topology, CBMS Regional Conference Series in Mathematics, vol. 43, American Mathematical Society, Providence, R.I., 1980. MR 565450
- Paik Kee Kim and Jeffrey L. Tollefson, Splitting the PL involutions of nonprime $3$-manifolds, Michigan Math. J. 27 (1980), no. 3, 259–274. MR 584691
- J. Milnor, A unique decomposition theorem for $3$-manifolds, Amer. J. Math. 84 (1962), 1–7. MR 142125, DOI 10.2307/2372800
- José M. Montesinos, Surgery on links and double branched covers of $S^{3}$, Knots, groups, and $3$-manifolds (Papers dedicated to the memory of R. H. Fox), Ann. of Math. Studies, No. 84, Princeton Univ. Press, Princeton, N.J., 1975, pp. 227–259. MR 0380802
- Seiya Negami, Irreducible $3$-manifolds with nontrivial $\pi _{2}$, Yokohama Math. J. 29 (1981), no. 2, 133–144. MR 649615
- Mitsuyuki Ochiai, $2$-sided embeddings of projective planes into $3$-manifolds, Trans. Amer. Math. Soc. 274 (1982), no. 2, 641–650. MR 675072, DOI 10.1090/S0002-9947-1982-0675072-3
- W. H. Row Jr., Irreducible $3$-manifolds whose orientable covers are not prime, Proc. Amer. Math. Soc. 34 (1972), 541–545. MR 296947, DOI 10.1090/S0002-9939-1972-0296947-2
- Friedhelm Waldhausen, Über Involutionen der $3$-Sphäre, Topology 8 (1969), 81–91 (German). MR 236916, DOI 10.1016/0040-9383(69)90033-0
Bibliographic Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 89 (1983), 545-550
- MSC: Primary 57N10; Secondary 57M99
- DOI: https://doi.org/10.1090/S0002-9939-1983-0715884-7
- MathSciNet review: 715884