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Some simple cases of Poincaré conjecture
Moto-o TAKAHASHI
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Moto-o TAKAHASHI
Institute of Mathematics The University of Tsukuba
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1980 Volume 32 Issue 2 Pages 373-397
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- Published: 1980 Received: July 20, 1978 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Correction information
Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) R. H. Bing, Necessary and sufficient conditions that a 3-manifold be S3, Ann. of Math., (2) 68 (1958), 17-37.
2) R. H. Bing, Some aspects of the topology of 3-manifolds related to the Poincaré conjecture, Lectures on Modern Mathematics, vol. 2, Wiley, New York, 1964, 93-128.
3) R. H. Bing and J. M. Martin, Cubes with knotted holes, Trans. Amer. Math. Soc., 155 (1971), 217-231.
4) J. S. Birman and H. M. Hilden, The homeomorphism problem for S3, Bull. Amer. Math. Soc., 79 (1973), 1006-1010.
5) J. S. Birman and H. M. Hilden, Heegaard splittings of branched coverings of S3, Trans. Amer. Math. Soc., 213 (1975), 315-352.
6) E. Brieskorn, Beispiele zur Differentialtopologie von Singularitäten, Invent. Math., 2 (1966), 1-14.
7) H. S. M. Coxeter, The abstract groups Gm.n.p, Trans. Amer. Math. Soc., 45 (1939), 73-150.
8) H. S. M. Coxeter, The abstract group G3,7,16, Proc. Edinburgh Math. Soc., (2), 13 (1962), 47-61.
9) H. S. M. Coxeter and W. O. Moser, Generators and relations for discrete groups, Springer, Berlin, 1957.
10) J. Hempel, A simply connected 3-manifold is S3 if it is the sum of a solid torus and the complement of a torus knot, Proc. Amer. Math. Soc., 15 (1964), 154-158.
11) T. Homma, On presentations of fundamental groups of 3-manifolds of genus 2, preprint.
12) E. J. Mayland Jr., A class of two-bridge knots with Property-P, preprint.
13) J. Milnor, On the 3-dimensional Brieskorn manifolds M(p, q, r), Knots, Groups, and 3-Manifolds (ed. by L.P. Neuwirth), 175-225.
14) M. Ochiai, On geometric reductions of homology 3-spheres of genus two, preprint.
15) H. Poincaré, Second complément a l'analysis situs, Proc. London Math. Soc., (2), 32 (1900), 277-308.
16) H. Poincaré, Cinquieme complément a l'analysis situs, Rend. Circ. Mat. Palermo, 18 (1904), 45-110.
17) R. Riley, Knots with parabolic property P, Quart. J. Math. Oxford (2), 25 (1974), 273-283.
18) J. Singer, Three-dimensional manifolds and their Heegaard diagrams, Trans. Amer. Math. Soc., 35 (1933), 88-111.
19) M. Takahashi, An alternative proof of Birman-Hilden-Viro's theorem, Tsukuba J. Math., 2 (1978), 27-34.
20) R. Osborne, The simplest closed 3-manifolds, Pacific J. Math., 74 (1978), 481-495.
21) M. Takahashi, Two-bridge knots have Property P, preprint.
Right : [1] R. H. Bing, Necessary and sufficient conditions that a 3-manifold be S3, Ann. of Math., (2) 68 (1958), 17-37.
[2] R. H. Bing, Some aspects of the topology of 3-manifolds related to the Poincaré conjecture, Lectures on Modern Mathematics, vol. 2, Wiley, New York, 1964, 93-128.
[3] R. H. Bing and J. M. Martin, Cubes with knotted holes, Trans. Amer. Math. Soc., 155 (1971), 217-231.
[4] J. S. Birman and H. M. Hilden, The homeomorphism problem for S3, Bull. Amer. Math. Soc., 79 (1973), 1006-1010.
[5] J. S. Birman and H. M. Hilden, Heegaard splittings of branched coverings of S3, Trans. Amer. Math. Soc., 213 (1975), 315-352.
[6] E. Brieskorn, Beispiele zur Differentialtopologie von Singularitäten, Invent. Math., 2 (1966), 1-14.
[7] H. S. M. Coxeter, The abstract groups Gm,n,p, Trans. Amer. Math. Soc., 45 (1939), 73-150.
[8] H. S. M. Coxeter, The abstract group G3,7,16, Proc. Edinburgh Math. Soc., (2), 13 (1962), 47-61.
[9] H. S. M. Coxeter and W. O. Moser, Generators and relations for discrete groups, Springer, Berlin, 1957.
[10] J. Hempel, A simply connected 3-manifold is S3 if it is the sum of a solid torus and the complement of a torus knot, Proc. Amer. Math. Soc., 15 (1964), 154-158.
[11] T. Homma, On presentations of fundamental groups of 3-manifolds of genus 2, preprint.
[12] E. J. Mayland Jr., A class of two-bridge knots with Property-P, preprint.
[13] J. Milnor, On the 3-dimensional Brieskorn manifolds M(p, q, r), Knots, Groups, and 3-Manifolds (ed. by L. P. Neuwirth), 175-225.
[14] M. Ochiai, On geometric reductions of homology 3-spheres of genus two, preprint.
[15] H. Poincaré, Second complément a l'analysis situs, Proc. London Math. Soc., (2), 32 (1900), 277-308.
[16] H. Poincaré, Cinquieme complément a l'analysis situs, Rend. Circ. Mat. Palermo, 18 (1904), 45-110.
[17] R. Riley, Knots with parabolic property P, Quart. J. Math. Oxford (2), 25 (1974), 273-283.
[18] J. Singer, Three-dimensional manifolds and their Heegaard diagrams, Trans. Amer. Math. Soc., 35 (1933), 88-111.
[19] M. Takahashi, An alternative proof of Birman-Hilden-Viro's theorem, Tsukuba J. Math., 2 (1978), 27-34.
[20] R. Osborne, The simplest closed 3-manifolds, Pacific J. Math., 74 (1978), 481-495.
[21] M. Takahashi, Two-bridge knots have Property P, preprint.
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