The mapping class group of manifolds which are like projective planes

TL;DR

This paper computes the mapping class group of certain simply-connected manifolds with specific homology, excluding four-dimensional cases, advancing understanding of their topological symmetries.

Contribution

It provides the first explicit computation of the mapping class group for these manifolds, extending previous knowledge beyond four dimensions.

Findings

Computed the mapping class group for manifolds with given homology

Excluded four-dimensional cases from the analysis

Enhanced understanding of topological symmetries of these manifolds

Abstract

In this paper we compute the mapping class group of simply-connected closed smooth manifolds $M$ with integral homology $H_{*}(M) \cong \mathbb Z \oplus \mathbb Z \oplus \mathbb Z$ provided that $\dim M \ne 4$.