## Osaka Journal of Mathematics

### Equivariant maps between representation spheres of cyclic ${p}$-groups

Ko Ohashi

#### Abstract

This paper deals with necessary conditions for the existence of equivariant maps between the unit spheres of unitary representations of a cyclic $p$-group $G$. T. Bartsch gave a necessary condition for some unitary representations of $G$ by using equivariant $K$-theory. We give two necessary conditions following Bartsch's approach. One is a generalization of Bartsch's result for any unitary representation of $G$ which does not contain the trivial representation. The other is a stronger necessary condition for some special cases.

#### Article information

Source
Osaka J. Math., Volume 54, Number 4 (2017), 647-659.

Dates
First available in Project Euclid: 20 October 2017

https://projecteuclid.org/euclid.ojm/1508486569

Mathematical Reviews number (MathSciNet)
MR3715353

Zentralblatt MATH identifier
06821129

#### Citation

Ohashi, Ko. Equivariant maps between representation spheres of cyclic ${p}$-groups. Osaka J. Math. 54 (2017), no. 4, 647--659. https://projecteuclid.org/euclid.ojm/1508486569

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