Remarks on the topology of folds

Remarks on the topology of folds
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Proc. Amer. Math. Soc. 123 (1995), 905-908

DOI: https://doi.org/10.1090/S0002-9939-1995-1283556-7

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We give some necessary conditions for a closed manifold to admit a smooth map into an Euclidean space with only fold singular points.

References

Richard L. W. Brown, A note on immersions up to cobordism, Illinois J. Math. 21 (1977), no. 2, 240–241. MR 436170

On singularities of folding type

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Takuo Fukuda, Topology of folds, cusps and Morin singularities, A fête of topology, Academic Press, Boston, MA, 1988, pp. 331–353. MR 928406
Mahito Kobayashi, Simplifying certain mappings from simply connected $4$-manifolds into the plane, Tokyo J. Math. 15 (1992), no. 2, 327–349. MR 1197101, DOI 10.3836/tjm/1270129459
Arunas Liulevicius, Immersions up to cobordism, Illinois J. Math. 19 (1975), 149–164. MR 377933
John W. Milnor and James D. Stasheff, Characteristic classes, Annals of Mathematics Studies, No. 76, Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1974. MR 0440554, DOI 10.1515/9781400881826
Osamu Saeki, Topology of special generic maps of manifolds into Euclidean spaces, Topology Appl. 49 (1993), no. 3, 265–293. MR 1208678, DOI 10.1016/0166-8641(93)90116-U
Osamu Saeki, Notes on the topology of folds, J. Math. Soc. Japan 44 (1992), no. 3, 551–566. MR 1167382, DOI 10.2969/jmsj/04430551
Kazuhiro Sakuma, On the topology of simple fold maps, Tokyo J. Math. 17 (1994), no. 1, 21–31. MR 1279567, DOI 10.3836/tjm/1270128185
Hassler Whitney, The singularities of a smooth $n$-manifold in $(2n-1)$-space, Ann. of Math. (2) 45 (1944), 247–293. MR 10275, DOI 10.2307/1969266