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Various topological complexities of small covers and real Bott manifolds

Part of: Classical Topics in Algebraic Topology

Published online by Cambridge University Press:  27 December 2023

Koushik Brahma ,
Bikramaditya Naskar ,
Soumen Sarkar  and
Subhankar Sau Open the ORCID record for Subhankar Sau [Opens in a new window]
Koushik Brahma
Affiliation:
Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, India (koushikbrahma95@gmail.com; bikramadityaix@gmail.com; soumen@iitm.ac.in)
Bikramaditya Naskar
Affiliation:
Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, India (koushikbrahma95@gmail.com; bikramadityaix@gmail.com; soumen@iitm.ac.in)
Soumen Sarkar
Affiliation:
Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, India (koushikbrahma95@gmail.com; bikramadityaix@gmail.com; soumen@iitm.ac.in)
Subhankar Sau
Affiliation:
Indian Statistical Institute, Kolkata 700108, India (subhankarsau18@gmail.com)
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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.

Keywords

topological complexitysmall coverreal bott manifold$\mathcal{D}$-topological complexitysymmetric topological complexity

MSC classification

Primary: 55M30: Ljusternik-Schnirelman (Lyusternik-Shnirel'man) category of a space
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , First View , pp. 1 - 26
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Copyright
Copyright © The Author(s), 2023. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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