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.
Gonçalves, D., Manzoli Neto, O., Spreafico, M. (2011). The Borsuk-Ulam theorem for homotopy spherical space forms. JOURNAL OF FIXED POINT THEORY AND ITS APPLICATIONS, 9(2), 285-294 [10.1007/s11784-011-0049-9].
The Borsuk-Ulam theorem for homotopy spherical space forms
Spreafico M
2011
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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