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Cobordism of combinatorial n – manifolds for n ≤ 8

Published online by Cambridge University Press:  24 October 2008

C. T. C. Wall
C. T. C. Wall
Affiliation:
Trinity College, Cambridge
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Extract

The object of this paper is two-fold: first to collect together the known facts about combinatorial cobordism in general, and then to calculate the groups for the first 8 dimensions. As in (29), we shall denote the unoriented and oriented cobordism groups in dimension n by and Ωn, and will distinguish the combinatorial from the differential case by affixes c, d.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 60 , Issue 4 , October 1964 , pp. 807 - 811
Copyright
Copyright © Cambridge Philosophical Society 1964

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References

REFERENCES

(1)Adams, J. F.On formulae of Thom and Wu. Proc. London Math. Soc. 11 (1961), 741–752.CrossRefGoogle Scholar
(2)Adams, J. F. On the J-homomorphism. (To appear.)Google Scholar
(3)Cairns, S. S.The manifold smoothing problem. Bull. American Math. Soc. 67 (1961), 237–238.CrossRefGoogle Scholar
(4)Hirsch, M. W.On combinatorial submanifolds of differentiable manifolds. Comment. Math. Helv. 36 (1961), 103–111.CrossRefGoogle Scholar
(5)Hirsch, M. W.Obstruction theories for smoothing manifolds and maps. Bull. American Math. Soc. 69 (1963), 352–356.CrossRefGoogle Scholar
(6)Kervaire, M. A. and Milnor, J. W.Groups of homotopy spheres. I. Ann. of Math. 77 (1963), 504–537.CrossRefGoogle Scholar
(7)Mazur, B.Séminaire de Topologie Combinatoire et Différéntielle de l' I.H.E.S., 1962/1963.Google Scholar
(8)Milnor, J. W.On manifolds homeomorphic to the 7-sphere. Ann. of Math. 64 (1956), 399–405.CrossRefGoogle Scholar
(9)Milnor, J. W.Sommes de variétés différentiables et structures différentiables de sphères. Bull. Soc. Math. France, 87 (1959), 439–444.Google Scholar
(10)Milnor, J. W.Differentiable structures on spheres. American J. Math. 81 (1959), 962–972.CrossRefGoogle Scholar
(11)Munor, J. W.Differentiable manifolds which are homotopy spheres (Princeton notes: 01 1959).Google Scholar
(12)Milnor, J. W.A procedure for killing homotopy groups of differentiable manifolds (Proc. Symp. on Pure Math. III, American Math. Soc: 1961).CrossRefGoogle Scholar
(13)Milnor, J. W.Microbundles and differentiable structures (Princeton notes: 09 1961).Google Scholar
(14)Munkres, J.Differentiable isotopies on the 2-sphere. Michigan Math. J. 7 (1960), 193–197.CrossRefGoogle Scholar
(15)Munkres, J.Obstructions to imposing differentiable structures (Princeton notes: 1960; see also Notices American Math. Soc. 7 (1960), 204).Google Scholar
(16)Munkres, J.Obstructions to the smoothing of piecewise differentiable homeomorphisms. Ann. of Math. 72 (1960), 521–554.CrossRefGoogle Scholar
(17)Rohlin, V. A. and Svarc, A. S.The combinatorial invariance of Pontrjagin classes. Dokl. Akad. Nauk SSSR, 114 (1957), 490–493 (in Russian).Google Scholar
(18)Smale, S.Diffeomorphisms of the 2-sphere. Proc. American Math. Soc. 10 (1959), 621–626.CrossRefGoogle Scholar
(19)Smale, S.Generalized Poincaré's Conjecture in dimensions greater than 4. Ann. of Math. 74 (1961), 391–406.CrossRefGoogle Scholar
(20)Smale, S.Differentiable and combinatorial structures on manifolds. Ann. of Math. 74 (1961), 498–502.CrossRefGoogle Scholar
(21)Smale, S.On the structure of manifolds. American J. Math. 84 (1962), 387–399.CrossRefGoogle Scholar
(22)Thom, R.Espaces fibrés en sphères et carrés de Steenrod. Ann. Sci. École Norm. Sup. 69 (1952), 109–181.CrossRefGoogle Scholar
(23)Thom, R.Quelques propriétés globales des variétés différentiables. Comment. Math. Helv. 28 (1954), 17–86.CrossRefGoogle Scholar
(24)Thom, R.Les classes caractéristiques de Pontrjagin des variétés triangulées (Symposium Internacional de Topologia Algebraica, Mexico: 1958).Google Scholar
(25)Thom, R.Des variétés triangulées aux variétés différentiables (Proc. Int. Congr. Math., 1958; Cambridge: 1960).Google Scholar
(26)Wall, C. T. C.Determination of the cobordism ring. Ann. of Math. 72 (1960), 292–311.CrossRefGoogle Scholar
(27)Wall, C. T. C.Killing the middle homotopy groups of odd dimensional manifolds. Trans. American Math. Soc. 103 (1962), 421–433.CrossRefGoogle Scholar
(28)Wall, C. T. C.Classification of (n – l)-connected 2n-manifolds. Ann. of Math. 75 (1962), 163–189.CrossRefGoogle Scholar
(29)Wall, C. T. C.Cobordism exact sequences for differential and combinatorial manifolds. Ann. of Math. 77 (1963), 1–15.CrossRefGoogle Scholar
(30)Whitehead, J. H. C.On C1-complexes. Ann. of Math. 41 (1940), 809–824.CrossRefGoogle Scholar
(31)Cerf, J. La nullité de π0 (Diff S3). Séminaire H. Cartan, nos. 8, 9, 10, 20, 21, Paris, 1962/63.Google Scholar