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Proceedings of the American Mathematical Society

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On a construction of Bredon

Author: Joseph Roitberg
Journal: Proc. Amer. Math. Soc. 33 (1972), 623-626
MSC: Primary 57D55
MathSciNet review: 0295370
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Abstract: Using a homotopy-theoretical description of a geometric pairing due to Bredon, we show how to rederive Bredon's results on the pairing. Furthermore, we are able to, in some sense, complete these results by combining the homotopy-theoretical approach with Sullivan's determination of the 2-primary Postnikov decomposition of the space G/PL.

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  • [1] G. E. Bredon, A $ {\Pi_\ast }$-module structure for $ {\Theta_\ast }$ and applications to transformation groups, Ann. of Math. (2) 86 (1967), 434-448. MR 36 #4570. MR 0221518 (36:4570)
  • [2] J. Levine, A classification of differentiable knots, Ann. of Math. (2) 82 (1965), 15-50. MR 31 #5211. MR 0180981 (31:5211)
  • [3] J. Roitberg, PL invariants on a smooth manifold, Thesis, New York University, New York, 1968.
  • [4] D. Sullivan, Triangulating homotopy equivalences, Thesis, Princeton University, Princeton, N.J., 1965.
  • [5] R. Williamson, Jr., Cobordism of combinatorial manifolds, Ann. of Math. (2) 83 (1966), 1-33. MR 32 #1715. MR 0184242 (32:1715)

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Keywords: Bredon pairing, differential structures on spheres, PL/O, Kervaire-Milnor construction $ {p_l}(\sigma )$, homotopy spheres bounding $ \pi $-manifolds, G/PL
Article copyright: © Copyright 1972 American Mathematical Society

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