Topology in seven dimensions

目标：该项目旨在给出一类7维空间的完整分类;即单连通自旋7-流形。给出了7-流形上G_2-结构分类的相关程序。 重要性：所提出的分类将是流形拓扑学的标志性成就，可能在几何学和数学物理学中都有应用。 预期成果：该项目将产生一系列在高质量期刊上发表的论文，并加强澳大利亚和联合王国之间的科学合作。 优点：该项目将通过在该国历史上没有代表的领域进行出色的研究来提高澳大利亚的研究声誉。

Aims: The project aims to give a complete classification of a certain class of 7-dimensional spaces; namely simply-connected spin 7-manifolds. We also present related programs classify G_2-structures on 7-manifolds. Significance: the proposed classification will be a signature achievement in the topology of manifolds, with applications likely in both geometry and mathematical physics. Expected outcomes: The project will produce a series of papers published in high quality journals and enhanced scientific collaboration between Australia and the United Kingdom. Benefits: The project will enhance Australia's research reputation by producing excellent research in a field not historically represented in the country.