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Additional structures in Smith theory


This paper is devoted to the development of the apparatus of Smith theory. In it we introduce operations ∪ and ∩ and also Poincare duality, which have not been considered previously. New connections are established between specific objects of Smith theory and objects of ordinary homology theory. The account is given for the case of a simplicial action on a finite simplicial space, the proofs are given briefly, most intermediate calculations are omitted.

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Literature cited

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    A. Borel et al., Seminar on Transformation Groups, Ann. Math. Stud., No. 46 (1960).

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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 122, pp. 17–23, 1982.

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Gusarov, M.N. Additional structures in Smith theory. J Math Sci 26, 1614–1618 (1984).

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  • Specific Object
  • Additional Structure
  • Simplicial Action
  • Homology Theory
  • Intermediate Calculation