The Capacity of Wedge Sum of Spheres of Different Dimensions

TL;DR

This paper computes the capacity of wedge sums of spheres of different dimensions and the complex projective plane, providing a negative answer to Borsuk's question about the capacity being determined solely by homology.

Contribution

It introduces a method to compute capacities for specific topological spaces and demonstrates that capacity is not solely determined by homology properties.

Findings

Capacity of wedge sums of spheres computed

Negative answer to Borsuk's question on homology and capacity

Capacity not solely determined by homology

Abstract

K. Borsuk in 1979, in the Topological Conference in Moscow, introduced the concept of the capacity of a compactum and raised some interesting questions about it. In this paper, during computing the capacity of wedge sum of finitely many spheres of different dimensions and the complex projective plane, we give a negative answer to a question of Borsuk whether the capacity of a compactum determined by its homology properties.