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Verschlingungszahlen von Fixpunktmengen in Darstellungsformen. II

Part of the Lecture Notes in Mathematics book series (LNM,volume 1217)

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

  1. a)

    The integers n(0) and n(1) are both odd and greater or equal to 5.

  2. b)

    The normal bundles ν i of the imbeddings ji, i=0, 1, are both trivial.

  3. 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. 1)

    the isotropy groups are 1, H0, H1,

  2. 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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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16824-9

  • Online ISBN: 978-3-540-47097-7

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