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Ramified coverings, orbit projections and symmetric powers

  • Albrecht Dold (a1)
Abstract

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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[1]Bredon G. E.. Introduction to Compact Transformation Groups (Academic Press, 1972).
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[4]Dold A. and Thom R.. Quasifaserungen und unendliche symmetrische Produkte. Ann. of Math. 67 (1958), 239281.
[5]Jerrard R. P.. Homology with multiple-valued functions applied to fixed points. Trans. AMS 213 (1975), 407427.
[6]Kahn D. S. and Priddy S. B.. Transfer and stable homotopy theory. Bull. AMS 78 (1972), 981987.
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[11]Smith L.. Transfer and ramified coverings. Math. Proc. Cambridge Philos. Soc. 93 (1983), 485493.
[12]Steenrod N.. Cohomology operations, and obstructions to extending continuous functions. Colloq. lectures (mimeogr.) (Princeton, 1957).
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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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