On 1-connected 8-manifolds with the same homology as $S^3\times S^5$

TL;DR

This paper classifies 1-connected 8-manifolds and Poincaré complexes with the same homology as $S^3 imes S^5$, addressing topological and smooth cases and discussing related questions.

Contribution

It provides a classification of 1-connected 8-dimensional manifolds and complexes with the same homology as $S^3 imes S^5$, including topological and smooth structures.

Findings

Classification of 1-connected 8-manifolds with given homology

Analysis of topological and smooth structures

Discussion of related open questions

Abstract

In this article, we classify 1-connected 8-dimensional Poincar\'e complexes, topological manifolds and smooth manifolds with the same homology as $S^3\times S^5$. Some questions of Escher-Ziller are also discussed.