Abstract
Let G=H0 × H1 be a product of two cyclic groups Hi of odd order. We show that there exist smooth actions of G on the standard sphere X=Sn(0)+n(1)+1 with the following properties:
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i)
The isotropy groups are 1, H0, and H1.
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ii)
The fixed point set XH i is a standard sphere Sn(i).
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iii)
The linking number k of the fixed point sets can be any integer in the kernel of the Swan homomorphisms sG:ℤ/|G|*→Ko(ℤG).
For certain values of thelinking number X does not have the equivariant homotopy type of a representation sphere.
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tom Dieck, T., Löffler, P. (1985). Verschlingung von Fixpunktmengen in Darstellungsformen. I. In: Smith, L. (eds) Algebraic Topology Göttingen 1984. Lecture Notes in Mathematics, vol 1172. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074431
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DOI: https://doi.org/10.1007/BFb0074431
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