Abstract
Let G= H0×H1 be a product of two cyclic groups of odd order. Let ji:Sn(i)→Sn(0)+n(1)+1, i=0, 1, be any two imbeddings of standard spheres into the standard sphere. Suppose
-
a)
The integers n(0) and n(1) are both odd and greater or equal to 5.
-
b)
The normal bundles ν i of the imbeddings ji, i=0, 1, are both trivial.
-
c)
The linking number k of j0(Sn(0)) and j1(Sn(1)) is a unit in ℤ/|G| and lies in the kernel of the Swan homomorphism sG : ℤ/|G|*→K(ℤG).
Then there is a smooth action of G on X=Sn(0)+n(1)+1 such that
-
1)
the isotropy groups are 1, H0, H1,
-
2)
the fixed point sets XH i are the spheres ji(Sn(i)), i=0, 1.
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© 1986 Springer-Verlag
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tom Dieck, T., Löffler, P. (1986). Verschlingungszahlen von Fixpunktmengen in Darstellungsformen. II. In: Jackowski, S., Pawałowski, K. (eds) Transformation Groups Poznań 1985. Lecture Notes in Mathematics, vol 1217. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072816
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DOI: https://doi.org/10.1007/BFb0072816
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