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Ramified coverings, orbit projections and symmetric powers

  • Albrecht Dold (a1)

L. Smith, in a recent paper [11], studied a class of maps X →Y which he called ramified coverings. Roughly speaking, these are maps with a multiple-valued inverse Y → SPdX; cf. 1·1. He showed that X → X/G is a ramified covering whenever a finite group G acts on X. Using results of [4] on infinite symmetric powers SPX of CW-complexes X he obtained transfer homomorphisms .

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[3] A. Dold . Homology of symmetric products and other functors of complexes. Ann. of Math. 68 (1958), 5480.

[4] A. Dold and R. Thom . Quasifaserungen und unendliche symmetrische Produkte. Ann. of Math. 67 (1958), 239281.

[5] R. P. Jerrard . Homology with multiple-valued functions applied to fixed points. Trans. AMS 213 (1975), 407427.

[6] D. S. Kahn and S. B. Priddy . Transfer and stable homotopy theory. Bull. AMS 78 (1972), 981987.

[7] S. Maxwell . Fixed points of symmetric product mappings. Proc. AMS 8 (1957), 808815.

[9] D. Puppe . A theorem on semi-simplicial monoid complexes. Ann. of Math. 70 (1959), 379394.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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