Homology, Homotopy and Applications

Volume 24 (2022)

Number 2

On generalized projective product spaces and Dold manifolds

Pages: 265 – 289

DOI: https://dx.doi.org/10.4310/HHA.2022.v24.n2.a13


Soumen Sarkar (Department of Mathematics, Indian Institute of Technology Madras, Chennai, Tamil Nadu, India)

Peter Zvengrowski (Department of Mathematics and Statistics, University of Calgary, Alberta, Canada)


D. Davis introduced projective product spaces in 2010 as a generalization of real projective spaces and discussed some of their topological properties. On the other hand, Dold manifolds were introduced by A. Dold in 1956 to study the generators of the non-oriented cobordism ring. Recently, in 2019, A. Nath and P. Sankaran made a modest generalization of Dold manifolds. In this paper we simultaneously generalize both the notions of projective product spaces and Dold manifolds, leading to infinitely many different classes of new smooth manifolds. Our main goal will be to study the integral homology groups, cohomology rings, stable tangent bundles, and vector field problems, on certain generalized projective product spaces and Dold manifolds.


Dold manifold, projective product space, toric manifold, small cover, homology group, cohomology ring, vector field, tangent space, Stiefel–Whitney characteristic class

2010 Mathematics Subject Classification

55N10, 55R25, 57R20, 57R25, 57R42

Received 16 October 2021

Received revised 22 November 2021

Accepted 22 November 2021

Published 24 August 2022