The cobordism classification of hypersurfaces in lens spaces

Creighton, J. H. C.

doi:10.1090/S0002-9939-1980-0568002-X

The cobordism classification of hypersurfaces in lens spaces
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by J. H. C. Creighton PDF

Proc. Amer. Math. Soc. 79 (1980), 499-504 Request permission

Abstract:

In Theorem A we classify by cobordism type the codimension one submanifolds of lens spaces $L_d^{2n + 1}$ (quotient of ${S^{2n + 1}}$ by the action of the dth roots of unity). A related immersion result is also obtained.

References

Glen E. Bredon and John W. Wood, Non-orientable surfaces in orientable $3$-manifolds, Invent. Math. 7 (1969), 83–110. MR 246312, DOI 10.1007/BF01389793
P. E. Conner and E. E. Floyd, Differentiable periodic maps, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Band 33, Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin-Göttingen-Heidelberg, 1964. MR 0176478
J. H. C. Creighton, An elementary proof of the classification of surfaces in the projective $3$-space, Proc. Amer. Math. Soc. 72 (1978), no. 1, 191–192. MR 515780, DOI 10.1090/S0002-9939-1978-0515780-2
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
René Thom, Quelques propriétés globales des variétés différentiables, Comment. Math. Helv. 28 (1954), 17–86 (French). MR 61823, DOI 10.1007/BF02566923