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Rational Integer Invariants of Regular Cyclic Actions

  Published:2004-03-01
 Printed: Mar 2004
  • Robert D. Little
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Abstract

Let $g\colon M^{2n}\rightarrow M^{2n}$ be a smooth map of period $m>2$ which preserves orientation. Suppose that the cyclic action defined by $g$ is regular and that the normal bundle of the fixed point set $F$ has a $g$-equivariant complex structure. Let $F\pitchfork F$ be the transverse self-intersection of $F$ with itself. If the $g$-signature $\Sign (g,M)$ is a rational integer and $n<\phi (m)$, then there exists a choice of orientations such that $\Sign(g,M)= \Sign F=\Sign(F\pitchfork F)$.
MSC Classifications: 57S17 show english descriptions Finite transformation groups 57S17 - Finite transformation groups
 

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