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Poincaré Transversality for Double Covers

Published online by Cambridge University Press:  20 November 2018

I. Hambleton  and
R. J. Milgram
I. Hambleton
Affiliation:
McMaster University, Hamilton, Ontario
R. J. Milgram
Affiliation:
McMaster University, Hamilton, Ontario
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Let π: X’ —” X be a double cover of 2n-dimensional Poincaré duality (PD) spaces. The double cover is a fibering so it is classified by a map f: X → RP1+1(l ≫ n). If the homotopy class of f contains a representative which is Poincaré transverse [5] to RPl ⊂ RPl+1, we say that w is Poincarésplit-table.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 6 , 01 December 1978 , pp. 1319 - 1330
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Browder, W., The Kervaire invariant, products and Poincaré transversality, Topology 12 (1973), 145–158.Google Scholar
2. Browder, W. and Livesay, R., Free involutions on homotopy spheres, Tohoku Math. J. 2ô (1972), 69–88.Google Scholar
3. Brumfiel, G., Madsen, I., and Milgram, R. J., PL characteristic classes and cobordism, Ann. of Math. 07 (1973), 83–159.Google Scholar
4. Brumfiel, G. and Milgram, R. J., Normal maps, covering spaces and quadratic functions, Duke Math. J. U (1977), 663–694.Google Scholar
5. Brumfiel, G. and Morgan, J., Homotopy theoretic consequences of N. Levitt's obstruction theory to transversality for spherical fibrations, Pac. J. Math. 67 (1976), 1–100.Google Scholar
6. Hambleton, I., Free involutions on 6-manifolds, Michigan Math. J. 22 (1975), 141–149.Google Scholar
7. Jones, L., Patch spaces, Ann. of Math. 97 (1973), 306–343.Google Scholar
8. Levitt, N., Poincaré duality cobordism, Ann. of Math. 06 (1972), 211–244.Google Scholar
9. Milgram, R. J., The mod(2) spherical characteristic classes, Ann. of Math. 02 (1970), 238–261.Google Scholar
10. Milgram, R. J., Strutt, J., and Zvengrowski, P., Projective stable stems of spheres, to appear.Google Scholar
11. Quinn, F., Surgery on Poincaré and normal spaces, Bull. Amer. Math. Soc. 78 (1972), 262–267.Google Scholar
12. Steenrod, N. and Epstein, D. B. A., Cohomology operations, Annals of Mathematics Studies 50 (Princeton, 1964).Google Scholar
13. Wall, C. T. C., Poincaré complexes I, Ann. of Math. 86 (1967), 213–245.Google Scholar
14. Wall, C. T. C., Classification of hermitian forms VI: Group rings. Ann. of Math. 103 (1976), 1–80.Google Scholar
15. Wall, C. T. C., Surgery on compact manifolds (Academic Press, 1970).Google Scholar