On the cardinality of the manifold set

TL;DR

This paper investigates the size of the set of manifolds homotopy equivalent to a given manifold and compares it to the structure set of that manifold.

Contribution

It provides new insights into the relationship between the cardinality of homotopy equivalent manifolds and the structure set of a manifold.

Findings

Establishes bounds on the cardinality of the manifold set

Shows the relationship between the manifold set and the structure set

Provides conditions under which the set is finite or infinite

Abstract

We study the cardinality of the set of manifolds homotopy equivalent to a given manifold M and compare it to the cardinality of the structure set of M.