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The relationship between homology and topological manifolds via homology transversality. (English) Zbl 0368.57003


MSC:

57P99 Generalized manifolds
57N55 Microbundles and block bundles
57Q10 Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc.
57Q35 Embeddings and immersions in PL-topology
57Q50 Microbundles and block bundles
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References:

[1] Brumfiel, G., Morgan, J.: Homotopy theoretic consequences of N. Levitt’s obstruction theory to transversality for spherical fibrations, Pacific J. of Math.67, 1-100 (1976) · Zbl 0343.55019
[2] Galewski, G., Stern, R.: Geometric transversality and bordism theories. Preprint
[3] Kirby, R., Siebenmann, L.: On the triangulation of manifolds and the Hauptvermutung. Bull. Amer. Math Soc.75, 742-749 (1969) · Zbl 0189.54701 · doi:10.1090/S0002-9904-1969-12271-8
[4] Kirby, R., Siebenmann, L.: Essays on topological manifolds, smoothings and triangulations. Annals of mathematics Studies, No. 88, Princeton New Jersey: Princeton University Press 1977 · Zbl 0361.57004
[5] Levitt, N.: Poincare’ duality cobordism. Ann. of Math.96, 211-244 (1972) · Zbl 0245.57006 · doi:10.2307/1970787
[6] Levitt, N., Morgan, J.: Transversality structures andPL structures on spherical fibrations. Bull. Amer. Math. Soc.78, 1064-1068 (1972) · Zbl 0267.55021 · doi:10.1090/S0002-9904-1972-13112-4
[7] Martin, N.: On the difference between homology and piecewise linear bundles. J. of London Math. Soc. (2)6, 197-204 (1973) · Zbl 0249.57007 · doi:10.1112/jlms/s2-6.2.197
[8] Martin, N.: Transverse regular maps of homology manifolds. Proc. Camb. Phil. Soc.74, 29-38 (1973) · Zbl 0257.57006 · doi:10.1017/S0305004100047745
[9] Martin, N., Maunder, C.: Homology cobordism bundles. Topology10, 93-110 (1971) · Zbl 0214.21804 · doi:10.1016/0040-9383(71)90032-2
[10] Matumoto, T.: Variétés simpliciales d’homologie et variétés topologiques métrisables. Thesis, Univ. de Paris-Sud, 91405, Orsay, 1976
[11] Matumoto, T., Matsumoto, Y.: The unstable difference between homology cobordism and piecewise linear block bundles. Tôhoku Math. J. (2)27, 57-68 (1975) · Zbl 0303.57009 · doi:10.2748/tmj/1178241034
[12] Maunder, C.: An H-cobordism theorem for homology manifolds. Proc. London Math. Soc. (3)25, 137-155 (1972) · Zbl 0248.57005 · doi:10.1112/plms/s3-25.1.137
[13] McCrory, C.: Cone complexes andPL transversality. Trans. Amer. Math. Soc.207, 269-291 (1975) · Zbl 0272.57009 · doi:10.1090/S0002-9947-1975-0400243-7
[14] Rourke, C., Sanderson, B.: Block bundles I. Ann. of Math. (2)87, 1-28 (1968) · Zbl 0215.52204 · doi:10.2307/1970591
[15] Rourke, C., Sanderson, B.: On topological neighborhoods. Composito Math.22, 387-424 (1970) · Zbl 0218.57005
[16] Rourke, C., Sanderson, B.: ?-sets. II. Block bundles and block fibrations. Quart. J. of Math.22, 465-485 (1971) · Zbl 0226.55020 · doi:10.1093/qmath/22.4.465
[17] Siebenmann, L.: Are non-triangulable manifolds triangulable? In Topology of Manifolds, J.C. Cantrell and C.H. Edwards, Jr., eds. Chicago, Ill.: Markham 1969 · Zbl 0297.57012
[18] Wall, C.T.C.: Surgery on compact manifolds. London Math. Soc. Monograph No. 1. London-New York: Academic Press 1970 · Zbl 0219.57024
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