Topology in seven dimensions

目的：该项目旨在给出一类7维空间的完全分类，即单连通自旋7-流形。我们还给出了7-流形上的G_2-结构分类的相关程序。 意义：拟议的分类将是流形拓扑学的一项标志性成果，可能在几何和数学物理中应用。 预期成果：该项目将发表一系列论文，发表在高质量的期刊上，并加强澳大利亚和联合王国之间的科学合作。 好处：该项目将通过在该国历史上没有代表性的领域产生优秀的研究成果，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.