On generalized complex projective product spaces
Abstract
Free circle action on manifolds has been explored in several articles. Gonzalez and Velasco considered some free circle actions on the finite product of spheres. In this paper, we introduce generalized complex projective product spaces, extending their definition and the concept of Dold manifolds. This produces infinitely many different classes of new smooth manifolds. First, we study the integral cohomology rings and stable tangent bundles on certain generalized complex-projective product spaces. Then, we discuss the product inequality for strongly equivaraint TC. We exhibit the closeness of the lower and upper bounds for the LS-category and topological complexity of several classes of generalized complex projective product spaces. In many cases, we compute the exact value of the LS-category.
Related
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BibTeX
@misc{daundkar2026generalized,
title = {{On generalized complex projective product spaces}},
author = {Navnath Daundkar and Soumen Sarkar},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30415},
eprint = {2608.30415},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30415},
}
RIS
TY - UNPB
TI - On generalized complex projective product spaces
AU - Navnath Daundkar
AU - Soumen Sarkar
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30415
UR - https://arxiv.org/abs/2608.30415
AB - Free circle action on manifolds has been explored in several articles. Gonzalez and Velasco considered some free circle actions on the finite product of spheres. In this paper, we introduce generalized complex projective product spaces, extending their definition and the concept of Dold manifolds. This produces infinitely many different classes of new smooth manifolds. First, we study the integral cohomology rings and stable tangent bundles on certain generalized complex-projective product spaces. Then, we discuss the product inequality for strongly equivaraint TC. We exhibit the closeness of the lower and upper bounds for the LS-category and topological complexity of several classes of generalized complex projective product spaces. In many cases, we compute the exact value of the LS-category.
ER -