Notes on the topology of folds

Osamu SAEKI

doi:10.2969/jmsj/04430551

Osamu SAEKI

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ジャーナルフリー

1992 年 44 巻 3 号 p. 551-566

DOI https://doi.org/10.2969/jmsj/04430551

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Published: 1992 Received: 1991/09/17 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 論文サブタイトル訂正内容: Wrong : Dedicated to Professor Haruo Suzuki on his 60th birthday

訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) T. Bröcker, Differentiable germs and catastrophes, Translated by L. Lander, London Math. Soc. Lect. Note Ser., 17, Cambridge Univ. Press, 1975.
2) J. M. Éliašberg, On singularities of folding type, Math. USSR Izv., 4 (1970), 1119-1134.
3) J. M. Éliasberg, Surgery of singularities of smooth mappings, Math. USSR Izv., 6 (1972), 1302-1326.
4) T. Fukuda, Topology of folds, cusps and Morin singularities, in “A Fete of Topology”. (eds. Y. Matsumoto, T. Mizutani and S. Morita), Academic Press, 1987, pp. 331-353.
5) M. Kobayashi, Simplifying certain mappings from simply connected 4-manifolds into the plane, preprint.
6) H. Levine, Elimination of cusps, Topology, 3 (suppl. 2) (1965), 263-296.
7) H. Levine, Mappings of manifolds into the plane, Amer. J. Math., 88 (1966), 357-365.
8) H. Levine, Classifying immersions into R⁴ over stable maps of 3-manifolds into R², Lecture Notes in Math., 1157, Springer, 1985.
9) J. N. Mather, Stability of C^∞ mappings: VI. The nice dimensions, in “Proc. Liverpool Singularities-Symposium I”. Lect. Notes in Math., 192, Springer, 1971, pp. 207-253.
10) B. Morin, Formes canoniques des singularités d'une application différentiables, C. R. Acad. Sc. Paris, 260 (1965), 5662-5665, 6503-6506.
11) O. Saeki, Topology of special generic maps of manifolds into Euclidean spaces, to appear in Topology Appl..
12) K. Sakuma, On special generic maps of simply connected 2n-manifolds into R³, to appear in Topology Appl..
13) S. Smale, Diffeomorphisms of the 2-sphere, Proc. Amer. Math. Soc., 10 (1959), 621-626.
14) N. Steenrod, Topology of fibre bundles, Princeton Univ. Press, 1951.
15) R. Thom, Les singularités des applications différentiables, Ann. Inst. Fourier (Grenoble), 6 (1955-56), 43-87.
16) J. H. C. Whitehead, The immersions of an open 3-manifold in Euclidean 3-space, Proc. London Math. Soc., 11 (1961), 81-90.

Right : [1] T. Bröcker, Differentiable germs and catastrophes, Translated by L. Lander, London Math. Soc. Lect. Note Ser., 17, Cambridge Univ. Press, 1975.
[2] J. M. Éliašberg, On singularities of folding type, Math. USSR Izv., 4 (1970), 1119-1134.
[3] J. M. Éliasberg, Surgery of singularities of smooth mappings, Math. USSR Izv., 6 (1972), 1302-1326.
[4] T. Fukuda, Topology of folds, cusps and Morin singularities, in “A Fete of Topology”. (eds. Y. Matsumoto, T. Mizutani and S. Morita), Academic Press, 1987, pp. 331-353.
[5] M. Kobayashi, Simplifying certain mappings from simply connected 4-manifolds into the plane, preprint.
[6] H. Levine, Elimination of cusps, Topology, 3 (suppl. 2) (1965), 263-296.
[7] H. Levine, Mappings of manifolds into the plane, Amer. J. Math., 88 (1966), 357-365.
[8] H. Levine, Classifying immersions into R⁴ over stable maps of 3-manifolds into R², Lecture Notes in Math., 1157, Springer, 1985.
[9] J. N. Mather, Stability of C^∞ mappings: VI. The nice dimensions, in “Proc. Liverpool Singularities-Symposium I”. Lect. Notes in Math., 192, Springer, 1971, pp. 207-253.
[10] B. Morin, Formes canoniques des singularités d'une application différentiables, C. R. Acad. Sc. Paris, 260 (1965), 5662-5665, 6503-6506.
[11] O. Saeki, Topology of special generic maps of manifolds into Euclidean spaces, to appear in Topology Appl..
[12] K. Sakuma, On special generic maps of simply connected 2n-manifolds into R³, to appear in Topology Appl..
[13] S. Smale, Diffeomorphisms of the 2-sphere, Proc. Amer. Math. Soc., 10 (1959), 621-626.
[14] N. Steenrod, Topology of fibre bundles, Princeton Univ. Press, 1951.
[15] R. Thom, Les singularités des applications différentiables, Ann. Inst. Fourier (Grenoble), 6 (1955-56), 43-87.
[16] J. H. C. Whitehead, The immersions of an open 3-manifold in Euclidean 3-space, Proc. London Math. Soc., 11 (1961), 81-90.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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