Various Topological Complexities of Small Covers and Real Bott Manifolds

2023/06/01 by Brahma, Koushik, Naskar, Bikramaditya, Sarkar, Soumen +1
#55M30 #57S12 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2306.00916

Abstract

In this paper, we compute the LS-category and equivariant LS-category of a small cover and its real moment angle manifold. We calculate a tight lower bound for the topological complexity of many small covers over a product of simplices. Then we compute symmetric topological complexity of several small covers over a product of simplices. We calculate the LS one-category of real Bott manifolds and infinitely many small covers.

Related

• LS-category and topological complexity of real torus manifolds and Dold manifolds of real torus type
• Small Covers, infra-nilmanifolds and positive curvature
• Higher equivariant and invariant topological complexity
• Small covers over wedges of polygons
• Small scale index theory, scalar curvature, and Gromov's simplicial norms