Involutions fixing ℝℙ^{𝕠𝕕𝕕}⊔ℙ(𝕙,𝕚), I

This paper studies the equivariant cobordism classification of all involutions fixing a disjoint union of an odd-dimensional real projective space R P j \mathbb {RP}^j with its normal bundle nonbounding and a Dold manifold P ( h , i ) P(h,i) with h > 0 h>0 and i > 0 i>0 . For odd h h , the complete analysis of the equivariant cobordism classes of such involutions is given except that the upper and lower bounds on codimension of P ( h , i ) P(h,i) may not be best possible; for even h h , the problem may be reduced to the problem for even projective spaces.