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Rational Integer Invariants of Regular Cyclic Actions

  • Robert D. Little (a1)

Abstract

Let $g:\,{{M}^{2n}}\,\to \,{{M}^{2n}}$ 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 $\text{Sign(g,}\,\text{M)}$ is a rational integer and $n\,<\,\phi (m)$ , then there exists a choice of orientations such that $\text{Sign}\,\text{(g,}\,\text{M)}\,\text{=}\,\text{Sign}\,\text{F}\,\text{=}\,\text{Sign}(F\,\pitchfork \,F)$ .

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References

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Rational Integer Invariants of Regular Cyclic Actions

  • Robert D. Little (a1)

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