Rational Integer Invariants of Regular Cyclic Actions

http://dx.doi.org/10.4153/CMB-2004-008-2
Canad. Math. Bull. 47(2004), 60-72

  Published:2004-03-01
 Printed: Mar 2004

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 $\Sign(g,M)= \Sign F=\Sign(F\pitchfork F)$.