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Isovariant maps from free -manifolds to representation spheres |
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| Authors: | Ikumitsu Nagasaki Fumihiro Ushitaki |
| Institution: | aDepartment of Mathematics, Kyoto Prefectural University of Medicine, 13 Nishitakatsukasa-cho, Taishogun Kita-ku, Kyoto 603-8334, Japan bDepartment of Mathematics, Faculty of Science, Kyoto Sangyo University, Kamigamo Motoyama, Kita-ku, Kyoto 603-8555, Japan |
| Abstract: | The isovariant version of Borsuk–Ulam type theorems has been studied by Wasserman and the first author. In this paper, first we consider the relation between the existence of Cn-isovariant maps from free Cn-manifolds to representation spheres and Borsuk–Ulam type inequalities for their dimensions. Our main result classifies the Cn-isovariant maps by Cn-isovariant homotopy types when a Borsuk–Ulam type inequality holds. For proving it, we use the multidegree of a Cn-equivariant map developed by the first author. |
| Keywords: | Borsuk–Ulam theorem Isovariant map Transformation groups Cyclic group action |
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