The Capacity of Some Classes of Polyhedra

TL;DR

This paper calculates the capacity of certain polyhedra, including products of spheres and lens spaces, and provides bounds for capacities of specific CW-complexes with cyclic fundamental groups.

Contribution

It extends the concept of capacity to new classes of polyhedra and offers explicit calculations and bounds for these topological spaces.

Findings

Capacity of product of two spheres computed

Capacity of lens spaces determined

Upper bound for capacity of $ Z_n$-complex established

Abstract

K. Borsuk in 1979, in the Topological Conference in Moscow, introduced the concept of the capacity of a compactum. In this paper, we compute the capacity of the product of two spheres of the same or different dimensions and the capacity of lense spaces. Also, we present an upper bound for the capacity of a $\mathbb{Z}_n$-complex, i.e., a connected finite 2-dimensional CW-complex with finite cyclic fundamental group $\mathbb{Z}_n$.