-manifolds which contain nonparallel projective planes

Author:
Tsuyoshi Kobayashi

Journal:
Proc. Amer. Math. Soc. **91** (1984), 314-318

MSC:
Primary 57N10; Secondary 57Q65

DOI:
https://doi.org/10.1090/S0002-9939-1984-0740193-0

MathSciNet review:
740193

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Abstract | References | Similar Articles | Additional Information

Abstract: We show that if a closed, connected -manifold with a Heegaard splitting of genus three contains mutually disjoint and nonparallel -sided projective planes, then the manifold is homeomorphic to the connected sum of and the twisted -sphere bundle over the circle.

**[1]**D. B. A. Epstein,*Projective planes in**-manifolds*, Proc. London Math. Soc. (3)**11**(1961), 469-484. MR**0152997 (27:2968)****[2]**J. Hempel,*-manifolds*, Ann. of Math. Stud., No. 86, Princeton Univ. Press, Princeton, N.J., 1976. MR**0415619 (54:3702)****[3]**W. Jaco,*Lectures on three manifold topology*, CBMS Regional Conf. Ser. in Math., Vol. 43, Amer. Math. Soc., Providence, R.I., 1980. MR**565450 (81k:57009)****[4]**W. B. R. Lickorish,*Homeomorphism of non-orientable two-manifolds*, Proc. Cambridge Philos. Soc.**59**(1963), 307-317. MR**0145498 (26:3029)****[5]**S. Negami,*Irreducible**-manifolds of genus*3*containing a**-sided projective plane*(preprint).**[6]**-,*Irreducible**-manifolds with non-trivial*, Yokohama Math. J.**29**(1981), 133-144. MR**649615 (83i:57004)****[7]**M. Ochiai,*-sided embeddings of projective planes into**-manifolds*, Trans. Amer. Math. Soc.**274**(1982), 641-650. MR**675072 (84c:57006)****[8]**-,*On Haken's theorem and its extension*, Osaka J. Math.**20**(1983), 461-468. MR**706246 (85c:57014)****[9]**W. H. Row,*Irreducible**-manifolds whose orientable covers are not prime*, Proc. Amer. Math. Soc.**34**(1972), 541-545. MR**0296947 (45:6006)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1984-0740193-0

Keywords:
Heegaard splittings,
nonparallel projective planes in -manifolds

Article copyright:
© Copyright 1984
American Mathematical Society