Irreducible 3-manifolds of genus 3 containing a 2-sided projective plane

Negami, Seiya

doi:10.1090/S0002-9939-1983-0715884-7

Irreducible $3$-manifolds of genus $3$ containing a $2$-sided projective plane
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Proc. Amer. Math. Soc. 89 (1983), 545-550 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

Involutions and isotopies of lens spaces

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