2020/10/22 by Soumen Sarkar, Sarkar, Soumen, Peter Zvengrowski +1
Mathematics · #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2010.11495
openalex publication_date 2020/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.