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Representation forms for metacyclic groups

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Abstract

In the following paper homotopy representations (h.r.) for metacyclic groups of the form

$$G = G_{p,q} = \left\langle {h,k|h^p = k^q = 1, khk^{ - 1} = h^d } \right\rangle $$

with dq≡1 modp, d≡1 mod p, H=<h>, K=<k>, odd primes p and q are studied. (Look at Gp.q as the easiest example of a non-abelian group).

As a main result a criterion is developed, which allows to decide (under suitable additional conditions on the dimension function, like gap hypothesis etc.), whether a given G-h.r. is relizable (up to oriented G-homotopy equivalence) as a smooth, compact representation form or not.

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  1. GKSS-Forschungszentrum, Institut für Physik, Max Planck Straße, D-2054, Geesthacht

    Christof Mackrodt

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  1. Christof Mackrodt
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Mackrodt, C. Representation forms for metacyclic groups. Manuscripta Math 73, 261–287 (1991). https://doi.org/10.1007/BF02567641

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  • DOI: https://doi.org/10.1007/BF02567641

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