On generalized projective product spaces and Dold manifolds

Abstract

Don Davis introduced projective product spaces in 2010 as a generalization of real projective spaces and studied several topological properties of these spaces. On the other hand, Dold manifolds were introduced by A. Dold long back in 1956 to study the generators of the non-oriented cobordism ring. From then on several interesting properties of Dold manifolds are studies. Recently, in 2019, Nath and Sankaran make a slight generalization of Dold manifolds. In this paper, we generalize the notion of projective product spaces and Dold manifolds which gives infinitely many different class of new manifolds. Our main goal here is to discuss integral homology groups, cohomology ring structures, stable tangent bundles and vector field problems on certain generalized projective product spaces and Dold manifolds.

On the LS-category and topological complexity of projective product spaces

“…This is a manifold of dimension dim(P n) = dim(S n) = n i and, when r = 1, the space P n coincides with the usual real projective space P n 1 . Recently, the notion of projective product space was used in [2] and generalized in [11].…”