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The Borsuk?CUlam theorem for homotopy spherical space forms |
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| Authors: | Daciberg L Gon?alves Mauro Spreafico Oziride Manzoli Neto |
| Institution: | 1. Departamento de Matem??tica - IME-USP, Caixa Postal 66281, Ag. Cidade de S?o Paulo, CEP 05314-970, S?o Paulo, SP, Brazil 2. Departamento de Matem??tica - ICMC-USP, University of S?o Paulo, S?o Carlos, Caixa Postal 668, S?o Carlos, SP, Brazil 3. Departamento de Matem??tica - ICMC-USP, University of S?o Paulo, S?o Carlos, Caixa Postal 668, S?o Carlos, SP, Brazil |
| Abstract: | In this work, we show for which odd-dimensional homotopy spherical space forms the Borsuk–Ulam theorem holds. These spaces are the quotient of a homotopy odd-dimensional sphere by a free action of a finite group. Also, the types of these spaces which admit a free involution are characterized. The case of even-dimensional homotopy spherical space forms is basically known. |
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