Involutions fixing ${\mathbb {RP}}^{\text {odd}} \sqcup P(h,i)$, II

Abstract:

This paper studies the equivariant cobordism classification of all involutions fixing a disjoint union of an odd-dimensional real projective space ${\mathbb {RP}}^j$ with its normal bundle nonbounding and a Dold manifold $P(h,i)$ with $h$ a positive even and $i>0$. The complete analysis of the equivariant cobordism classes of such involutions is given except that the upper and lower bounds on the codimension of $P(h,i)$ may not be best possible. In particular, we find that there exist such involutions with nonstandard normal bundle to $P(h,i)$. Together with the results of part I of this title (Trans. Amer. Math. Soc. 354 (2002), 4539–4570), the argument for involutions fixing ${\mathbb {RP}}^{\text {odd}}\sqcup P(h,i)$ is finished.